The subjects in Group 1 are those with the 50 lowest four-digit numbers. Group 2 is given the remaining subjects.
An experiment that is conducted at random?What a Random Situation Is Exactly. Any clearly defined procedure that yields an observable result that could not be entirely predicted beforehand is considered a random experiment. In order to avoid any ambiguity or surprise, a random experiment must be clearly defined.
List the subjects in alphabetical order by name.
A four-digit number at random, between 0001 and 9999 (inclusive), should be given to each subject using a table of random numbers.
Leaving out 4 digit that have already been allocated.
The subjects in Group 1 are those with the 50 lowest four-digit numbers. Group 2 is given the remaining subjects.
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A family buys a studio apartment for $200,000. They pay a down payment of $20,000. a. Their down payment is what percent of the purchase price? b. What percent of the purchase price would a $90,000 down payment be?
Answer:
A. 20,000 is 10% of 200,000, so the percentage of the purchase price is 10%.
B. 90,000 is 45% of 200,000, so the percentage of the 90,000 down payment is 45%.
Suppose Shen is the only seller in the market for bottled water and Manuel is the only buyer. The following lists show the value Manuel places on a bottle of water and the cost Shen incurs to produce each bottle of water:Manuel's Value -------------------------- Shen's CostsValue of first bottle: $7 ------------- Cost of first bottle: $1Value of second bottle: $5 ------- Cost of second bottle: $3Value of third bottle: $3 ------------ Cost of third bottle: $5Value of fourth bottle: $1 ---------- Cost of fourth bottle: $7The following table shows their respective supply and demand schedules:Price ------------ Quantity Supplied --------- Quantity DemandedMore than $7 ----------- 4 ----------------------------- 0$5 to $7 ----------------- 3 ----------------------------- 1$3 to $5 ----------------- 2 ----------------------------- 2$1 to $3 ------------------ 1 ----------------------------- 3$1 or less ---------------- 0 ----------------------------- 4Use Shen's supply schedule and Manuel's demand schedule to find the quantity supplied and quantity demanded at prices of $2, $4, and $6. Enter these values in the following table.Price ----------- Quantity Supplied ---------- Quantity Demanded2 ------------------------- ? ----------------------------- ?4 ------------------------- ? ----------------------------- ?6 ------------------------- ? ----------------------------- ?A price of _____ brings supply and demand into equilibrium.At the equilibrium price, consumer surplus is $___, producer surplus is $___, and total surplus is $___.If Shen produced and Manuel consumed one less bottle of water, total surplus would _____.If instead, Shen produced and Manuel consumed one additional bottle of water, total surplus would _____.
If Shen produced and Manuel consumed one additional bottle of water, total surplus would be $2
What is the law of Supply and Demand?The law of supply and demand combines two fundamental economic ideas that describe how changes in the price of a resource, commodity, or product affect its supply and demand.
Supply grows as the price rises, but demand drops. In contrast, as the price falls, supply is constrained and demand is increased.
Demand and supply levels for different prices can be displayed as curves on a graph. The intersection of these curves symbolizes the process of price discovery in the marketplace, as it indicates the balance, or market-clearing price, at which demand equals supply.
According to the law of demand, demand for a good or resource will decrease as its price increases and increase as its price decreases.
How to solve?
Price ------ Quantity Supplied ----- Quantity Demanded
2 --------------------- 1 ------------------------- 3
4 --------------------- 2 ------------------------ 2
6 --------------------- 3 ------------------------ 1
4 (quantity supplied = quantity demanded = 2)
4 ($7>$4 and $5>$4, $3<$4<$5, area above price line but under curve if price line was at $4, $7-$4=$3, $5-$4=$1, $3+$1=$4); 4 ($1<$4 and $3<$4, $3<$4<$5, area below price line and under curve if price line at $4, $4-$1=$3, $4-$3=$1, $3+$1=$4); 8 ($4 from consumer surplus + $4 from producer surplus)
fall (equilibrium = 2, 2-1=1, Shen: quantity supplied = 1 -> $2, Manuel: quantity demanded = 1 -> $6, total surplus = producer surplus + consumer surplus = ($4-$1)+($7-$4)=$6, $8>$6)
rise (equilibrium = 2, 2+1=3, Manuel: quantity demanded = 3 -> $2, Shen: quantity supplied = 3 -> $6, total surplus = consumer surplus + producer surplus = ($3-$2)+($7-$6)=$2, $8>$2, $6>$2)
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A garden has 8 rows of plants. each row has 12 tomato plants and 3 bean plants. how many more tomato plants than bean plants are in the garden?
Answer: 72
Step-by-step explanation: because 8 x 12 = 96 and 3 x 8 = 24
96 - 24 = 72
a sample of bacteria is decaying according to a half-life model. if the sample begins with 500 bacteria, and after 16 minutes there are 350 bacteria, after how many minutes will there be 40 bacteria remaining?
After approximately 113 minutes, there will be only 40 bacteria remaining.
Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.
N(t) = N₀(1/2)^(t/T)
where N(t) = amount of substance remaining after time t
N₀ = initial amount of substance
t = time
T = half-life
If the sample begins with 500 bacteria, and after 16 minutes there are 350 bacteria, then
N₀ = 500, and N(t) = 350 when t = 16 minutes
Substitute the given values and solve for the half-life.
N(t) = N₀(1/2)^(t/T)
350 = 500(1/2)^(16/T)
T = 31.09 minutes
Using the formula, solve for t when n(t) = 40.
N(t) = N₀(1/2)^(t/T)
40 = 500(1/2)^(t/31.09)
t = 113.30 minutes
t ≅ 113 minutes
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uppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour. (a) choose the appropriate null and alternative hypotheses if the mean cost for the current production method is $220 per hour.
Tn the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂
What are alternative hypotheses?An assertion used in statistical inference experiments is known as the alternative hypothesis.
It is indicated by Ha or H1 and runs counter to the null hypothesis.
Another way to put it is that it is only a different option from the null.
An alternative theory in hypothesis testing is a claim that the researcher is testing.
The initial assertion that forms the null hypothesis frequently rests on research from the past or expert knowledge.
According to the alternative hypothesis, a population parameter is either less, larger, or different from the value predicted by the null hypothesis.
So, the new production method supposedly lowers the mean operating cost per hour.
The following are the hypothesis when comparing the average production costs of the new production method (μ₁) with the old production method (μ₂):
H₀: μ₁ ≥ μ₂
H₁: μ₁ < μ₂
Therefore, in the given situation, the appro[riate null hypotheses and alternative hypotheses are: H₀: μ₁ ≥ μ₂a and H₁: μ₁ < μ₂
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Make a conjecture about the value
Points A, B, and C are collinear,
and D is between B and C.
Answer :not fully correct
cStep-by-step explanation:
7 cups to 20 ounces ratio
Answer:7:20
Step-by-step explanation:
HELP PLEASE, I’ll give points and mark brainliest
Find the volume of a right circular cone that ha a height of 13,8 cm and a bae with a circumference of 15. 8 m
Answer: V=πr2h
3
Step-by-step explanation: Your spelling is a bit off
Please help now asap !!!!!!!!!
Answer:
80
usually estimate is rounded 1 significant figure, 0.9 is rounded to 1, and 82 is rounded to 80.
1*80 is 80
Which of the following describes the correct order of events?
A
E
U
D
1. African Americans are denied the right to vote.
2. African Americans organize marches for voting rights in Alabama.
3. The Voting Rights Act is signed.
1. The Voting Rights Act is signed.
2. African Americans are denied the right to vote.
3. African Americans organize marches for voting rights in Alabama.
1. African Americans are denied the right to vote.
2. The Voting Rights Act is signed.
3. African Americans organize marches for voting rights in Alabama.
1. The Voting Rights Act is signed.
2. African Americans organize marches for voting rights in Alabama.
3. African Americans are denied the right to vote.
Answer:
A
Step-by-step explanation:
describes a good place
PLEASE HELP
Which values of a, b, and c correctly represent the answer in simplest form?
a = 1 b= 5 c= 9
a = 10 b =18 c=1
a =9 b =5 c=1
a =1 b =10 c=18
The values of a, b and c in the mixed fractions are 1, 5 and 9 respectively.
How to simplify fractions?The fractions are mixed fractions . let's convert it to improper fraction be we simplify its.
A mixed fraction is a whole number and a proper fraction combined. Improper fractions are defined as fractions for which the numerator is greater than the denominator.
Therefore, let's solve the fractions as follows:
[tex]3\frac{1}{2}[/tex] ÷ [tex]2\frac{1}{4}[/tex]
[tex]3\frac{1}{2} = \frac{7}{2}[/tex]
[tex]2\frac{1}{4} = \frac{9}{4}[/tex]
Therefore,
[tex]\frac{7}{2} (\frac{4}{9} ) = \frac{28}{18} = 1\frac{10}{18} = 1\frac{5}{9}[/tex]
Hence,
a = 1
b = 5
c = 9
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Graph the opposite of − 7 on the number line.
Answer:
Positive seven.
Step-by-step explanation:
Go past zero to normal seven.
Answer:positive 7
Step-by-step explanation:
Sam and Rohan's families are driving to Chicago, Illinois, from Orlando, Florida. Sam's
family is driving a direct route of 1,157 miles at 65 mph. Rohan and his family are driving
through Charlotte, North Carolina and will drive 1,250 miles at 70 mph.
1.
2.
At this rate, how many hours will it take Sam's family to get to Chicago, Illinois?
(Round your answer to the tenths place. )
How many hours will it take Rohan's family to arrive in Chicago, Illinois? (Round
your answer to the tenths place. )
(1) It will take 17.8 hours for Sam's family to get to Chicago, Illinois .
(2) Rohan's family will take 17.9 hours to arrive in Chicago, Illinois .
In the question ,
it is given that ,
For Sam's Family ,
total distance to be covered is = 1157 miles ,
the average speed is given to be = 65 mph .
By the formula of Speed , Distance and Time ,
we get ,
65 = 1157/t
t = 1157/65
t = 17.8 hours .
For Rohan's family ,
total distance to be covered is = 1250 miles ,
the average speed is given to be = 70 mph ,
By the formula of Speed , Distance and Time ,
we get ,
70 = 1250/t
t = 1250/70
t = 17.9 hours
Therefore , Sam's family will take 17.8 hours and Rohan's family will take 17.9 hours .
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solve for y ! ~
[tex] \rm \: y = 5 \pm58[/tex]
The solution for y in the expression is y = -53 and y = 63
How to determine the solution for y?From the question, the expression is given as
y = 5 ± 58
We start by expanding the expression
So, we have the following representation
y = 5 - 58 and y = 5 + 58
Evaluate the sum and the difference of the like terms in the above expression
So, we have the following representation
y = -53 and y = 63
Hence, the solution is
y = -53 and y = 63
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if a woodworker builds 3/7 chair in 3/4 hour, how long does it takes the woodworker to build 1 chair
Answer:
it would take him 4/7 of an hour
Step-by-step explanation:
Enlarge the triangle by scale factor -3 with centre (3,3)
The triangles when enlarged by a scale factor of 3 the final image is at the coordinates: (7, 3), (5, 3), and (7, 7)
How to find the coordinates of the imageThe coordinates of the preimage are
(5, 3), (4, 3), and (5, 5)
translate to the origin
= (5 - 3, 3 - 3), (4 - 3, 3 - 3), and (5 - 3, 5 - 3)
= (2, 0), (1, 0), and (2, 2)
dilate about the origin
2 * { (2, 0), (1, 0), and (2, 2) }
(4, 0), (2, 0), and (4, 4)
translate back to usual position
(4 + 3, 0 + 3), (2 + 3, 0 + 3), and (4 + 3, 4 + 3)
(7, 3), (5, 3), and (7, 7)
Therefore the image is at (7, 3), (5, 3), and (7, 7)
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suppose that, as in exercises 5.11 and 5.79, y1 and y2 are uniformly distributed over the triangle shaded in the accompanying diagram. (–1, 0) (1, 0) (0, 1) y1 y2 a find cov(y1, y2). b are y1 and y2 independent? (see exercise 5.55.) c find the coefficient of correlation for y1 and y2. d does your answer to part (b) lead you to doubt your answer to part (a)? why or why not?
Using the definition of covariance, Cov(Y(1)Y(2))= 0. From the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2)). So, it can be concluded that Uncorrelated variables need not be independent.
Given joint probability function of Y(1) and Y(2), is
p(Y(1)*Y(2)) = 1/3, for (y(1)*y(2)) = (- 1, 0), (0, 1), (1, 0)
So Y(1), takes random variable -1,0,1.
And Y(2) takes random variable 0,1.
Y(2)|Y(1) -1 0 1
0 1/3 0 1/3
1 0 1/3 0
From the table:
The marginal probability function of Y(1) is;
P(Y(1)=y(1)) = ∑P(Y(1)=y(1)), y(1)= -1,0,1. That is;
Y(1)=y(1) -1 0 1
P(Y(1)=y(1)) 1/3 1/3 1/3
From the definition of expectation,
E[y(1)]= [tex]\Sigma_{y_{1}}[/tex] y(1)P(Y(1)=y(1))
E[y(1)]= -1(1/3)+0(1/3)+1(1/3)
E[y(1)]= -1/3+0+1/3
E[y(1)]= 0
The marginal probability mass function of y(2) is
P(Y(2)=y(2)) = ∑P(y(1)y(2)), y(2)= 0,1. That is;
Y(2)=y(2) 0 1
[tex]P_{Y(2)}[/tex](y(2)) 2/3 1/3
Now E[y(2)]= [tex]\Sigma_{y_{2}}[/tex] y(2)P(Y(2)=y(2))
E[y(2)]= 0(2/3)+1(1/3)
E[y(2)]= 1/3
And
E[y(1)y(2)]= [tex]\Sigma_{y_{1}}\Sigma_{y_{2}}[/tex] y(1)y(2)P(y(1)y(2))
E[y(1)y(2)]= -1(0)(1/3)+0(1)(1/3)+1(0)(1/3)
E[y(1)y(2)]= 0
From the definition of covariance.
The Cov(Y(1)Y(2))= E[Y(1)Y(2)]-E[Y(1)E[Y(2)]
Cov(Y(1)Y(2))= 0-1/3 (0)
Cov(Y(1)Y(2))= 0
The Cov(Y(1)Y(2))=0, implies that the two variables are uncorrelated. But from the given information the two variables Y(1), and Y(2), are dependent and, p(y(1)y(2)) ≠ P(y(1))p(y(2))
Hence, it can be concluded that Uncorrelated variables need not be independent.
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To participate in a baeball league, the required equipment for each player i a glove, a hat, and a pair of cleat. A glove cot $50. 95 , a hat cot $20. 95 , and a pair of cleat cot $25. 95. What i the total cot for a team of 10 player?
The total cost for a team of 10 player in a baseball league is $978.5.
Explain the term unitary method?By using the unitary technique, we may calculate the price of a specific unit from the values of several other units, and then we can use this value to assess the cost of the necessary number of units.For the stated question,
The cost of each equipment for each player is-
glove = $50. 95 hat = $20. 95 pair of cleat = $25. 95Thus,
Total cost for each player = $50. 95 + $20. 95 + $25. 95
Total cost for each player = $97.85
Total number of player in a baseball league = 12
Total cost for team = 10 x $97.85
Total cost for team = $978.5
Thus, the total cost for a team of 10 player in a baseball league is $978.5.
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Peggy pays an annual fee of $10.75 to belong to an online music club and download songs at a reduced price. Last year she downloaded 105 songs altogether. Non-members pay $0.35 more per song download than members. Suppose Daniel is not a member of the club and downloaded 85 songs last year. If Daniel and Peggy both paid the same total amount, what is the cost per download for members and for non-members? Let x
represent the cost of downloading a song for members. Set up and solve an equation. Show your work.
Help! Due Tonight
The solution of the algebraic equation for the cost of downloading a song for members is x = $0.95
How to set up and solve an equation for the cost of downloading a song for members?Given that:
1. Peggy pays an annual fee of $10.75. Last year she downloaded 105 songs
2. Non-members pay $0.35 more per song download than members
3. Daniel is not a member of the club and downloaded 85 songs last year
Let x represent the cost of downloading a song for members
Thus, the cost of a song for Peggy will be x
From statement 2: the cost of a song for Daniel will be x+0.35
The algebraic equation for the total amount for Peggy will be:
A = 105x + 10.75
The algebraic equation for the total amount for Daniel will be:
A = 85(x+0.35)
If Daniel and Peggy both paid the same total amount, we can say:
105x + 10.75 = 85(x+0.35)
105x + 10.75 = 85x + 29.75
105x - 85x = 29.75 - 10.75
20x = 19
x = 19/20
x = 0.95
Thus, the cost of a song for member is $0.95
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Help PLEASE!!!! Like in the next 15 mins!
The values of A, B, C and D are 55.04ft² ,9184.50ft , 75.36ft and 38.46ft², the A(C-D)+B= 11214.00
What are circumference and area of a circle?Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = πr2.
Circumference of a circle is the perimeter of a circle. It can be calculated as C= πd or 2πr
calculating A, the area of the circle is 3.14×8²= 200.96
the area of the square= l×l= 16×16= 256
area of the shaded part = 256-200.96= 55.04ft²
calculating B, since the maintenance worker moved round 3 times
3C = 3πd= 3.14×975×3 = 9184.50ft
calculating C
circumference of 3 bowls
= 3πd= 3×3.14×8= 75.36ft
calculating D
area= πr²= 3.14×3.5²
= 38.46ft²
therefore A(C-D)+B= 55(75.36-38.46)+9184.50
= 2029.5+9184.5
= 11214.00
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Complete the equation so that it has no solution.
Enter the correct answer in the box.
6x+5=3 +
plus what to equal to no solution
Answer:
-3
Step-by-step explanation:
6x + 5 = 0 - there are no solutions...
Answer:
Step-by-step explanation:
-1/3
Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level. Which one of the following is the value of t?.
The value of t while considering a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level is ±1.685.
Given:
Consider a right-tailed test (upper tail) and a sample size of 40 at the 95% confidence level.
we are asked to determine the t value:
The directional hypothesis is:
Hₐ : µ > µ₀
The sample size is, n = 40.
The significance level is:
α = 1-0.95 = 0.05
Use the t-table to compute the right-tailed t-critical value as follows:
tₐ,₍ₙ₋₁₎ = t₀.₀₅,₍₄₀₋₁₎
= t₀.₀₅,₃₉
≈ t₀.₀₅,₄₀
= 1.684
≈ 1.685
The value is positive since the directional hypothesis suggests that the test is right tailed.
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Sharon discovered $2.95
worth of nickels and dimes.
If she has a total of 37 coins, how many of each kind of coin does she possess?
Answer:15 nickels 22 dimes
Step-by-step explanation:
the liabilities of departments are normally distributed with an unknown population mean and standard deviation. if a random sample of 36 departments is taken to estimate the mean liabilities, what t-score should be used to find a 95% confidence interval estimate for the population mean?
Critical value with 35 degrees of freedom at 0.05 Los = 2.030
Given information,
Departmental liabilities have a mean and standard deviation that are unknown for the population. What t-score should be used to establish a 95% confidence interval estimate for the population mean if a random sample of 36 departments is utilized to estimate the mean liabilities?
Here,
By assuming a 95% confidence interval and by considering the t-value we have,
Therefore;
Critical value at 0.05 Los with 35 degrees of freedom =2.030
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A radioactive compound with mass 100 grams decays at a rate of 5. 8% per hour. Which equation represents how many grams of the compound will remain after 2 hours?.
On solving the question, we got that - [tex]P(t) = P_{100e^{-0.058t} }[/tex] grams of radioactive compound will remain after 2 hours.
What is Radioactive compunds?Chemicals known as radionuclides (also known as radioactive materials) have unstable atoms in their center. Changes in the nucleus help them maintain stability, spontaneous fission, emission of alpha particles, or conversion of neutrons to protons or the reverse.
Future value is the issue at hand. If weight is measured in grams and time is measured in years, then [tex]P(t) = P_{0e^{-rt} }[/tex] with [tex]P_{0} = 100[/tex] and r = 0.058
Therefore,
[tex]P(t) = P_{100e^{-0.058t} }[/tex]
Will remain after 2 hours.
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If there are 48 lollipops and 60 candy bars for a gift bag, fill out all of the possible ratios of lollipops to candy bars that could be made
Answer:
Step-by-step explanation:
The ratio formula is given as a:b = a/b for any two quantities, let's say a and b. Given that a and b are separate amounts for two quantities, the combined total quantity is denoted by (a + b).
There are 48 lollipops and 6 candy bars for a gift bag.
Then the possible ratios of lollipops to candy bars are:
( 48 / 6 ) ÷ ( 2 / 2) = ( 24 / 3 )
( 48 / 6 ) ÷ ( 3 / 3) = ( 16 / 2 )
( 48 / 6 ) ÷ ( 6 / 6) = ( 8 / 1 )
There are 48 lollipops for every 6 candy bars.
There are 24 lollipops for every 3 candy bars.
There are 16 lollipops for every 2 candy bars.
There are 8 lollipops for every 1 candy bar.
the standard error of estimate measures the accuracy of a prediction. group startstrue or falsetrue, unselectedfalse, unselected
The statement is true that is the standard error of estimate measures the accuracy of a prediction.
Given that,
We have a statement that is the standard error of estimate measures the accuracy of a prediction.
We have to find is the statement is true are false.
We know that,
What is standard error?The SE formula is used to determine how accurately a sample represents a population. The sample mean's departure from the specified population is provided as follows,
Formula for standard error
S.E=S/√n
Where, n is the number of observations and S is the standard deviation.
Therefore, The statement is true that is the standard error of estimate measures the accuracy of a prediction.
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For Daniel's lemonade recipe, 4 lemons are required to make 16 cups of lemonade. At what rate are lemons being used in lemons per cup of lemonade?
The rate at which lemons being used in lemons per cup of lemonade is 0.25 lemons per cup
RatioA ratio compares values. A ratio says how much of one thing there is compared to another thing.
Rate of Change
Rate of change is the value at which the rest of the time.
Let the rate of lemon per cup of lemonade be x
Total lemon = 4
For a cup of lemonade =16
Rate of lemon per cup of lemonade
x = 4/16
x= 0.25.
Therefore, the required rate of lemon per cup of lemonade is 0.25 lemons per cup
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6 balls are drawn with replacement from a bag containing 7 red balls and 3 black balls. (round your answers to five decimal places.)
(a) Find the probability that 2 of the balls will be red. (b) Find the probability that all 6 balls will be black. (c) Find the probability that at least 4 of the balls will be black.
Step-by-step explanation:
"with replacement". that means any pulled ball is returned into the bag, and we have the full 7+3 = 10 balls to pull from every time.
remember, a probability is always
desired cases / totally possible cases
(a) 2 back will be red. I understand this, that exactly 2 balls will be red (not fewer, not more).
to get exactly 2 red balls we get 2 red balls and 4 black balls.
the probability for such a single event is
7/10 × 7/10 × 3/10 × 3/10 × 3/10 × 3/10 = 49×81/1000000 =
= 0.003969
because the probably to get a red ball (one from 7 out of 10) is 7/10.
the probability to get a black ball is 3/10.
how many different such single events are possible ?
as many as there are combinations to pick 2 out of 6 :
C(6, 2) = 6! / (2! × (6-2)!) = 6! / (2 × 4!) =
= 6×5 / 2 = 3×5 = 15
so, the probability to get exactly 2 red balls is
15 × 0.003969 = 0.059535 ≈ 0.05954
(b)
the probability of all 6 balls being black is
3/10 × 3/10 × 3/10 × 3/10 × 3/10 × 3/10 =
= 3⁶/1000000 = 0.000729 ≈ 0.00073
(c)
"at least 4 black balls" means exactly 4, or exactly 5, or exactly 6 balls are black.
that means we need to calculate all 3 probabilities and add them (non-overlapping "or"-cases means addition of probabilities, "and" cases mean multiplication as above).
to get exactly 4 black balls (= 4 black balls and 2 red balls) is the same as (a) : 0.059535
to get exactly 5 black balls (= 5 black balls and 1 red ball) in one specific constellation is
3⁵/10⁵ × 7/10 = 243×7/1000000 = 0.001701
and we have C(6, 5) possible constellations
C(6, 5) = 6! / (5! × (6-5)! = 6! / 5! = 6
the total probability to get exactly 5 black balls is
6 × 0.001701 = 0.010206
to get exactly 6 black balls is (b) : 0.000729
the probability to get at least 4 black balls is
0.059535 + 0.010206 + 0.000729 =
= 0.07047