A student sets up the following equation to convert a measurement. Fill in the missing part of the equation
Answers
Answer:
We have the equation:
(14 N/mm)*X = Y N/cm
So we want to transform 1/mm to 1/cm.
We know that:
10mm = 1cm
1 = 10mm/1cm (we want to have mm on the numerator, so it cancelates with the mm in the denominator)
then the conversion is from 1/mm to 1/cm is:
X = 10mm/cm
then we have:
(14N/mm)*(10mm/cm) = 140 N/cm
Related Questions
A computer retail store has 1414 personal computers in stock. A buyer wants to purchase 33 of them. Unknown to either the retail store or the buyer, 33 of the computers in stock have defective hard drives. Assume that the computers are selected at random.
A) In how many different ways can the 3 computers be chosen? 120
B) What is the probability that exactly one of thecomputers will be defective?
C) What is the probability that at least one of thecomputers selected is defective?
Answers
Answer:
a) 364 ways
b) 45.33% probability that exactly one of the computers will be defective.
c) 54.67% probability that at least one of the computers selected is defective.
Step-by-step explanation:
The computers are chosen without replacement, so we use the hypergeometric distribution to solve this question.
Hypergeometric distribution:
The probability of x sucesses is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of sucesses.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this question:
14 computers, so N = 14.
3 defective, so k = 3.
3 will be purchesed, so n = 3.
A) In how many different ways can the 3 computers be chosen?
3 from a set of 14. So
[tex]C_{14,3} = \frac{14!}{3!(14-3)!} = 364[/tex]
364 ways
B) What is the probability that exactly one of thecomputers will be defective?
This is P(X = 1).
[tex]P(X = 1) = h(1,14,3,3) = \frac{C_{3,1}*C_{11,2}}{C_{14,3}} = 0.4533[/tex]
45.33% probability that exactly one of the computers will be defective.
C) What is the probability that at least one of the computers selected is defective?
Either none is, or at least one is. The sum of the probabilities of these events is 1. So
[tex]P(X = 0) + P(X \geq 1) = 1[/tex]
We want [tex]P(X \geq 1)[/tex]. Then
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = 0) = h(0,14,3,3) = \frac{C_{3,0}*C_{11,3}}{C_{14,3}} = 0.4533[/tex]
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.4533 = 0.5467[/tex]
54.67% probability that at least one of the computers selected is defective.
The function h(t) = –16t2 + 28t + 500 represents the height of a rock t seconds after it is propelled by a slingshot.
What does h(3.2) represent?
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
Answers
Answer:
h(3.2) represents the height of the rock 3.2 seconds after it is propelled. Remember, h(t) represents the height of a rock t seconds after it is propelled.
Answer:
D
Step-by-step explanation:
the height of the rock 3.2 seconds before it reaches the ground
the time it takes the rock to reach the ground, or 3.2 seconds
the time it takes the rock to reach a height of 3.2 meters
the height of the rock 3.2 seconds after it is propelled
Solve for b. -11b+7 = 40 Two step equations
Answers
Step-by-step explanation:
-11b + 7 = 40
-11b = 40 - 7
-11b = 33
b = 33/-11
b = - 3
Rebecca is a real estate agent who would like to find evidence supporting the claim that the population mean market value of houses in the neighborhood where she works is greater than $250,000. To test the claim, she randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922. The test statistic t for a hypothesis test of H0 : μ = 250.000 versus Ha : μ > 250.000 is t 2.34 , which has 34 degrees of freedom. If 0.01
A) Fail to reject the null hypothesis that the true population mean market value of houses in the neighborhood where Rebecca works is equal to $250,000.
B) Reject the null hypothesis that the true population mean market value of houses in the neighborhood where Rebecca works is equal to $250,000.
C) There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.
D) There is not enough evidence at the α-_ 0.05 level of significance to suggest that the true population mean market value of houses in the neighborhood where Rebecca works is not equal to $250,000.
Answers
Answer:
There is enough evidence at the α-: 0.05 level of significance to support the claim that the true population mean market value of houses in the neighborhood where Rebecca works is greater than $250,000.
Step-by-step explanation:
We are given that Rebecca randomly selects 35 houses in the neighborhood and finds that the sample mean market value is $259,860 with a sample standard deviation of $24.922.
Let [tex]\mu[/tex] = population mean market value of houses in the neighborhood.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = $250,000 {means that the population mean market value of houses in the neighborhood where she works is equal to $250,000}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] > $250,000 {means that the population mean market value of houses in the neighborhood where she works is greater than $250,000}
The test statistics that would be used here One-sample t-test statistics because we don't know about population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean market value = $259,860
s = sample standard deviation = $24,922
n = sample of houses = 35
So, the test statistics = [tex]\frac{259,860-250,000}{\frac{24,922}{\sqrt{35} } }[/tex] ~ [tex]t_3_4[/tex]
= 2.34
The value of t-test statistic is 2.34.
Also, P-value of the test statistics is given by;
P-value = P([tex]t_3_4[/tex] > 2.34) = 0.0137
Since our P-value is less than the level of significance as 0.0137 < 0.05, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the population mean market value of houses in the neighborhood where she works is greater than $250,000.
Solve for x in the equation x squared + 10 x + 12 = 36. x = –12 or x = 2 x = –11 or x = 1 x = –2 or x = 12 x = –1 or x = 11
Answers
Answer:
-12 or x = 2.
Step-by-step explanation:
Teaching descriptive statistics. A study compared five different methods for teaching descriptive statistics. The five methods were traditional lecture and discussion, programmed textbook instruction, programmed text with lectures, computer instruction, and computer instruction with lectures. 45 students were randomly assigned, 9 to each method. After completing the course, students took a 1-hour exam.
a. What are the hypotheses for evaluating if the average test scores are different for the different teaching methods?
b. What are the degrees of freedom associated with the F-test for evaluating these hypotheses?
c. Suppose the p-value for this test is 0.0168. What is the conclusion?
Answers
Answer:
Step-by-step explanation:
a. The hypotheses are:
Null hypothesis: the average test scores are the same for the different teaching methods.
Alternative hypothesis: the average test scores are different for the different teaching methods.
b. To determine the degree of freedom for the F test: we must find two sources of variation such that we have two variances. The two sources of variation are: Factor (between groups) and the error (within groups) and add this up. Or use (N - 1). N is number in sample
c. With a p value of of 0.0168 and using a standard significance level of 0.05, we will reject the null hypothesis as 0.0168 is less than 0.05 and conclude that the average test scores are different for the different teaching methods.
Jalisa earned $71.25 today babysitting, which is $22.50 more than she earned babysitting yesterday. The equation d + 22.50 = 71.25 can be used to represent this situation, where d is the amount Jalisa earned babysitting yesterday. Which is an equivalent equation that can be used to find the amount Jalisa earned babysitting yesterday? 71.25 minus 22.50 = d 71.25 + 22.50 = d d + 71.25 = 22.50 d minus 22.50 = 71.25
Answers
Answer:
71.25 - 22.50 = d
Step-by-step explanation:
To find how much she earned yesterday, we subtract how much she earned today by the amount more she earned.
Answer:
A
Step-by-step explanation:
Benny is trying to learn how to ride a bike, but is terrified of falling. He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1; if he learns to ride a bike by using a bike without training wheels, his probability of falling is 0.5, and if he uses a unicycle, his probability of falling is 0.8. Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.
a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?
b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?
Answers
Answer:
a) 7.14% probability that Benny was learning to ride a bike using the training wheels
b) 28% probability that Benny was learning to ride a bike using the training wheels
Step-by-step explanation:
Bayes Theorem:
Two events, A and B.
[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]
In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.
Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.
a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?
So
Event A: Benny fell
Event B: Benny was using training wheels.
The probability that Benny was using each of these 3 methods is equal
This means that [tex]P(B) = \frac{1}{3}[/tex]
He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;
This means that [tex]P(A|B) = 0.1[/tex]
Probability of falling:
1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.
1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5
1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then
[tex]P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667[/tex]
So
[tex]P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714[/tex]
7.14% probability that Benny was learning to ride a bike using the training wheels
b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?
Similar as above, just some probabilities change.
Event A: Benny fell
Event B: Benny was using training wheels.
The probability that he was using training wheels is 0.7
This means that [tex]P(B) = 0.7[/tex]
He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;
This means that [tex]P(A|B) = 0.1[/tex]
Probability of falling:
0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.
0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5
0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then
[tex]P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25[/tex]
So
[tex]P(B|A) = \frac{0.7*0.1}{0.25} = 0.28[/tex]
28% probability that Benny was learning to ride a bike using the training wheels
A bag contains 6 red balls and 9 black balls. Two balls are drawn, one after the other with replacement. Find the probability that
a. Both are of the same colours
b. Both are of different colours
Answers
Answer:
a) 13/25
b) 12/15
Step-by-step explanation:
a) Since it is with replacement, the chance of them being both the same colour will be
P(both red) + P(both black) = (6/15*6/15) + (9/15*9/15)
= 13/25
b) If they are both different colours, then we will be working out
P(both colours) = (6/15*9/15)*2 = 12/25 (Its *2 because the other way of pulling both colours is 9/15*6/15 which is the same but flipped)
Another way of working this question out is
P(1-All red or all blue) which from above we know that All red or all blue is 13/25 so
P(1-All red or all blue) = 1 - 13/25 = 12/25
A model with 12 squares labeled exact value and 3 squares labeled error. A model with 18 squares labeled exact value and 3 squares labeled Error. Which is true of the models? Check all that apply. Both exact values are less than the approximate value. The percent errors are the same. The top model has a greater percent error. The bottom model has a greater percent error. The absolute error is the same for both.
Answers
Answer:
a,c,e
Step-by-step explanation:
on edge-
Answer:
The answer is A, C, E
All math teachers are smart. Ms. Smith is your math teacher, so she is smart. What type of reasoning is this? inductive or deductive
Answers
Answer:
I believe it is Inductive Reasoning.
Step-by-step explanation:
Inductive Reasoning is a type of logical thinking that involves forming generalizations based on specific incidents you've experienced, observations you've made, or facts you know to be true or false.
Deductive Reasoning is a basic form of valid reasoning.
It take Donna 15 minutes to complete 3 levels of Candy Crush. At this rate, how many levels will she complete in 3 hours?
Answers
Answer: she will have 36 levels completed
Find the common ratio for this geometric sequence. 243, 27, 3, 1/3, 1/27.
Answers
Answer:
1/9
Step-by-step explanation:
Since each next term is 1/9 of the last, the common ratio is 1/9. This can be confirmed by the fact that 243*1/9=27, 27*1/9=3, 3*1/9=1/3, and so on. Hope this helps!
How do I solve 24-27?
Answers
Answer:
-3
Step-by-step explanation:
You find the difference between the numbers, which is 3. Then you make it negative since 24 is less than 27.
To assess the accuracy of a laboratory scale, a standard weight known to weigh 1 gram is repeatedly weighed a total of n times How large should n be so that a 95% confidence interval for µ has a margin of error of ± 0.0001?
Answers
Answer:
[tex]n=(\frac{1.960(1)}{0.0001})^2 =384160000[/tex]
So the answer for this case would be n=384160000 rounded up to the nearest integer
Step-by-step explanation:
We know the following info:
[tex] ME = 0.0001[/tex] represent the margin of error desired
[tex] \sigma= 1[/tex] we assume that the population deviation is this value
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =0.0001 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} \sigma}{ME})^2[/tex] (b)
The critical value for 95% of confidence interval now can be founded using the normal distribution. If we use the normal standard distribution or excel we got: [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(1)}{0.0001})^2 =384160000[/tex]
So the answer for this case would be n=384160000 rounded up to the nearest integer
I rlly rlly rlly need help! Complete the following proof. Given: Points R, S, T, Q on circle O Prove: m\overarc RS + m\overarc ST + m\overarc TQ + m\overarc RQ
Answers
Answer:
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]
Step-by-step explanation:
As we can see in the figure that
The R, S, T ,and Q are the points on the circle O.
Also
The measurement of the circular arc is equivalent to the measurement of the angle at the center of the arc
So by this
[tex]m(\widehat{RS})=m(\angle ROS)[/tex]
[tex]m(\widehat{ST})=m(\angle SOT)[/tex]
[tex]m(\widehat{TQ})=m(\angle TOQ)[/tex]
m(major arc RQ) = m(∠QOR)
So,
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = m(\angle ROS)+m(\angle SOT)+m(\angle TOQ)+m(\angle QOR)[/tex]
And as we know that
All angles sum = 360°
Therefore
[tex]m(\widehat {RS})+m(\widehat{ST})+m(\widehat{TQ}) + m(major\ arc RQ) = 360\ degree[/tex]
Find the value of x and the value of y.
A r= 15, y = 10/3
B. r=20, p=10/3
C. x=20/3, y = 513
D. r=15, y =53
Answers
Answer:
Step by step solution:
Please answer this correctly
Answers
Answer:
yes
Step-by-step explanation:
not every person is going to have the same opinion, so it is yes.
// have a great day //
Answer:
Yes, because if Pedro asked them the question "what do you think of public transportation?" the majority would probably say that they like it or something along those lines. This is biased because there may be other city inhabitants who don't think very highly of public transportation. Basically, what I'm trying to say is that not everyone will have the same opinion.
A random sample of 4000 U.S. citizens yielded 2280 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.
Answers
Answer:
[tex] n= 4000[/tex] represent the sample size of citizens selected
[tex] X= 2280[/tex] represent the people who are in favor of gun control legislation
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p= \frac{2280}{4000}= 0.57[/tex]
Step-by-step explanation:
For this problem we have the following info given:
[tex] n= 4000[/tex] represent the sample size of citizens selected
[tex] X= 2280[/tex] represent the people who are in favor of gun control legislation
And for this case we want to estimate the roportion of all Americans who are in favor of gun control legislation and for this case we can use the following formula:
[tex]\hat p =\frac{X}{n}[/tex]
And replacing we got:
[tex]\hat p= \frac{2280}{4000}= 0.57[/tex]
please solve this for me T_T
If
[tex]x - \sqrt{a} [/tex]
is a factor of
[tex]2 {x}^{4} - 2 {a}^{2} {x}^{2} - 3 {x} + 2 {a}^{3} - 2 {a}^{2} + 3[/tex]
then find the value of
[tex]a[/tex]
Answers
Answer:
[tex]\boxed{\sf \ a = 1 \ }[/tex]
Step-by-step explanation:
let s assume that a >=0 so that we can take the square root
if [tex]x-\sqrt{a}[/tex] is a factor of this expression it means that [tex]\sqrt{a}[/tex] is a root of it
it comes
[tex]2*(\sqrt{a})^4-2*a^2*(\sqrt{a})^2-3*\sqrt{a}+2*(\sqrt{a})^3-2(\sqrt{a})^2+3=0[/tex]
So
[tex]2*a^2-2*a^3-3*\sqrt{a}+2*a*\sqrt{a}-2*a+3=0[/tex]
we can notice that 1 is a trivial solution as
2-2-3+2-2+3=0
so the answer is 1
let s double check
if a =1
the expression is
[tex]2x^4-2x^2-3x+2-2+3=2x^4-2x^2-3x+3[/tex]
and we can write
[tex]2x^4-2x^2-3x+3=(x-1)(2x^3+2x^2-3)[/tex]
so 1 is the correct answer
box + box + box equals to 30
OPTIONS (1,3,5,7,9,11,13,15)
Answers
Step-by-step explanation:
[tex] \boxed{3!} + \boxed{9 }+ \boxed{15} = 30 \\ \because \: 3! = 3 \times 2 \times 1 = 6 \\ \therefore \: 6 + 9 + 15 = 30[/tex]
can 10/12 be simplified
Answers
Answer:
5/6
Step-by-step explanation:
10/12
Divide the top and bottom by 2
10/2 = 5
12/2 =6
the fraction becomes 5/6
Answer :
10/12
Reduce the fraction
= 5/6
george cut a cake into 8 equal pieces. what is the unit fraction for the cake
Answers
Answer: 1/8
Step-by-step explanation:
Unit Fractions: A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer. A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Example of Unit Fractions: 1/1, 1/2, 1/3, 1/4 ,1/5, etc.
Hope this helps! Please mark as brainliest!
The unit fraction of the cake is 1/8
What is a unit fraction?A unit fraction is a rational number written as a fraction where the numerator is one and the denominator is a positive integer.
A unit fraction is therefore the reciprocal of a positive integer, 1/n.
Examples are 1/1, 1/2, 1/3, 1/4, 1/5, etc.
Given that, George cut a cake into 8 equal pieces, we need to find the unit fraction for the cake
Since, George cut the cake in 8 equal pieces so, 1 part will be shown by 1/8 of the cake, that mean 1/8 is one unit of the cake, we can say that 1/8 is the unit of the whole cake.
Hence, the unit fraction of the cake is 1/8
Learn more about unit fractions, click;
https://brainly.com/question/15326565
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this is a grade 4 maths question. i need help with doing a model from this question as well. thank you! —————————————————- a rope was cut into 2 pieces. The first piece was twice the length of the second piece. If the first piece was 5m 50cm long what was the length of the rope before it was cut
Answers
Answer:825cm
Step-by-step explanation:550cm/2=275cm
275*3=825cm
What is g(x)?
5-
X
10
-10
Answers
Answer: g(x)= -x^2
Step-by-step explanation:
BRO THIS IS THE MOST BASIC ALGEBRA 1 !?!?!?!?!?!?!?!
assume that when adults with smartphones are randomly selected, 45% use them in meetings or classes. If 6 adult smartphone users are randomly selected, find the probability that exactly 3 of them use their smartphones in meetins or classes.
Answers
Answer:
0.3032
Step-by-step explanation:
Use binomial probability.
P = nCr p^r q^(n-r)
where n is the number of trials,
r is the number of successes,
p is the probability of success,
and q is the probability of failure (1-p).
P = ₆C₃ (0.45)³ (0.55)³
P = 0.3032
A tire manufacturer is measuring the margin of error in the thickness of their tires to make sure it is within safety limits. Overall, the tires' thickness is normally distributed with a mean of 0.45 inches and a standard deviation of 0.05 inches. What thickness separates the lowest 5% of the means from the highest 95% in a sample size of 65 tires
Answers
Answer:
Z = -1.65
[tex]\bar x \approx 0.44 \ inches[/tex]
Step-by-step explanation:
The main objective is to compute the data for the Z value and determine the [tex]\bar x[/tex] of the sample distribution
Given that;
the tires' thickness is normally distributed with a mean μ = 0.45 in
standard deviation σ = 0.05 in
sample size = 65 tires
Also; we are being told that the thickness separates the lowest 5% of the means from the highest 95%
∴
P(Z < Z) =0.05
From the Z- table
P(Z < -1.645) = 0.05
Z = -1.65
Similarly;
Let consider [tex]\bar x[/tex] to be the sample mean;
Then:
mean [tex](\mu_{\bar x}) = \mu = 0.45[/tex]
standard deviation[tex](\sigma_{\bar x} ) = \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=\dfrac{0.05}{\sqrt{65}}[/tex]
= 0.00620174
By applying the Z-score formula:
x = μ + ( Z × σ )
[tex]\bar x = \mu _{\bar x} +(Z * \sigma _{\bar x})[/tex]
[tex]\bar x = 0.45 + (-1.65 *0.00620174)[/tex]
[tex]\bar x= 0.439767129[/tex]
[tex]\bar x \approx 0.44 \ inches[/tex]
There are 5 gallons of distilled water in science supplies. If 8 students each use an equal amount of distilled water and there is 1 gallon left in supplies, how much will each student get?
Answers
Answer:
0.5 gallon
Step-by-step explanation:
let x refer to students
5 = 8x + 1
8x = 4
x= 0.5 gallon
Find the most suitable system of coordinates to describe cylindrical shell of height 10 determined by the region between two cylinders with the same center, parallel rulings, and radii of 2 and 6 respectively.
Answers
Answer:
The answer is explained below
Step-by-step explanation:
We have a system that would be a cylindrical shell with a certain length. I will attach an allusive image, they ask us to determine which would be the most suitable system of coordinates:
Most suitable surface is cylindrical annular for this annular 30 disk most suitable coordinate system would be Cylindrical Coordinate System as one at coordinate "z" remains constant and that would be advantageous
The probability a person has read a book in the past year is 0.81. The probability a person is considered a millennial is 0.28. The probability a person has read a book in the past year and is considered a millennial is 0.25
(a) Find P(Millennial | Read a Book).
(b) Find P(Not Millennial | Did Not Read a Book).
(c) Are being considered a millennial and having read a book in the past year independent events? Justify your answer mathematically.
Answers
Answer:
(a) P(Millennial | Read a Book) = 0.3086
(b) P( Not Millennial | Did Not Read a Book) = 0.8421
(c)
P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)
0.25 = 0.81 × 0.28
0.25 ≠ 0.2268
Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.
Step-by-step explanation:
The probability a person has read a book in the past year is 0.81.
P(Read a Book) = 0.81
The probability a person is considered a millennial is 0.28.
P(Millennial) = 0.28
The probability a person has read a book in the past year and is considered a millennial is 0.25.
P(Millennial and Read a Book) = 0.25
(a) Find P(Millennial | Read a Book)
Recall that Multiplicative law of probability is given by
P(A ∩ B) = P(B | A) × P(A)
P(B | A) = P(A ∩ B) / P(A)
For the given case,
P(Millennial | Read a Book) = P(Millennial and Read a Book) / P(Read a Book)
P(Millennial | Read a Book) = 0.25 / 0.81
P(Millennial | Read a Book) = 0.3086
(b) Find P(Not Millennial | Did Not Read a Book)
P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)
Where
∵ P(A' and B') = 1 - P(A or B)
P(Not Millennial and Did Not Read a Book) = 1 - P(Millennial or Read a Book)
∵ P(A or B) = P(A) + P(B) - P(A and B)
P(Millennial or Read a Book) = P(Read a Book) + P(Millennial) - P(Millennial and Read a Book)
P(Millennial or Read a Book) = 0.81 + 0.28 - 0.25
P(Millennial or Read a Book) = 0.84
So,
P(Not Millennial and Did Not Read a Book) = 1 - 0.84
P(Not Millennial and Did Not Read a Book) = 0.16
Also,
∵ P(A') = 1 - P(A)
P(Did Not Read a Book) = 1 - P(Read a Book)
P(Did Not Read a Book) = 1 - 0.81
P(Did Not Read a Book) = 0.19
Finally,
P( Not Millennial | Did Not Read a Book) = P(Not Millennial and Did Not Read a Book) / P(Did Not Read a Book)
P( Not Millennial | Did Not Read a Book) = 0.16/0.19
P( Not Millennial | Did Not Read a Book) = 0.8421
(c) Are being considered a millennial and having read a book in the past year independent events? Justify your answer mathematically.
Mathematically, two events are considered to be independent if the following relation holds true,
P(A and B) = P(A) × P(B)
For the given case,
P(Millennial and Read a Book) = P(Read a Book) × P(Millennial)
0.25 = 0.81 × 0.28
0.25 ≠ 0.2268
Since the relation doesn't hold true, therefore, being considered a millennial and having read a book in the past year are not independent events.