Suppose that Haley encounter two traffic lights on her commute to GGC campus. Based on
her past experience, she judge that the probability is 0.35 that the first light will be red when she gets to it,
0.45 that the second light will be red, and 0.20 that both lights will be red. Let R1 denote the event that the
first light is red, and let R2 denote the event that the second light is red.
a) Determine the probability that at least one light will be red. (Show how you calculate this.)
b) Determine the conditional probability that the second light will be red given that the first light is
red. (Show how you calculate this.)
c) Are the events R1 and R2 independent? Justify your answer numerically.
d) Are the events R1 and R2 disjoint (mutually exclusive)? Justify your answer numerically.
Answer:
Explained below.
Step-by-step explanation:
The information provided is,
P (R₁) = 0.35
P (R₂) = 0.45
P (R₁ ∩ R₂) = 0.20
(a)
Compute the probability that at least one light will be red as follows:
P (at least one light will be red) = P (R₁ ∪ R₂)
= P (R₁) + P (R₂) - P (R₁ ∩ R₂)
= 0.35 + 0.45 - 0.20
= 0.60
Thus, the probability that at least one light will be red is 0.60.
(b)
Compute the conditional probability that the second light will be red given that the first light is red as follows:
[tex]P(R_{2}|R_{1})=\frac{P(R_{1}\cap R_{2})}{P(R_{1})}[/tex]
[tex]=\frac{0.20}{0.35}\\\\=0.571428\\\\\approx 0.57[/tex]
Thus, the conditional probability that the second light will be red given that the first light is red is 0.57.
(c)
If two events, say A and B are independent then:
P (A|B) = P (A).
The value of P (R₂ | R₁) = 0.57.
And the value of P (R₂) = 0.45
P (R₂ | R₁) ≠ P (R₂)
Thus, the events R₁ and R₂ are not independent.
(d)
If two events, say A and B are mutually exclusive then:
P (A ∩ B) = 0
The value of P (R₁ ∩ R₂) = 0.20.
Thus, the events R₁ and R₂ are not mutually exclusive.
Please help ASAP! All questions.
Answer:
I think i don't really know its been awhile for me.
Step-by-step explanation:
But i think you do 2 x 10 and what ever you get from that you multiply by 5 and what get from that you divide by 24.
I may not be right.
So please don't hate i tried.
You are playing a video game. For each diamond you collect, you earn 110 points. You also earn 80 bonus points by completing the level in less than 2 minutes. You need to earn more than 1620 points to continue on to the next level. Write and solve an inequality that represents the numbers d of diamonds you must collect in less than 2 minutes to advance to the next level.
Answer:
110d + 80 > 1620
d > 14
Step-by-step explanation:
The amount of points from collecting diamonds can be represented by 110d, since you get 110 points for each diamond, d
Add 80 to this to represent the bonus points.
Use a greater than inequality, because you have to get more than 1620 points.
Put this all together:
110d + 80 > 1620
Then, solve for d:
110d + 80 > 1620
110d > 1540
d > 14
So, you have to collect more than 14 diamonds in less than 2 minutes in order to advance to the next level.
**PLEASE HELP THIS IS DUE TODAY** when the sun's declination is at the highest point, what direction does the sun rise and set?
The bowling lanes charge an hourly fee for bowling and $2 to rent shoes for the day. Gerry rented shoes and bowled for 2 hours and was charged $12.
Which equation represents the cost, f(x), of bowling as a function of x, the number of hours of bowling?
Of(x) = 4x + 3
Of(x) = 2x + 2
Of(x) = 5x - 2
O f(x) = 5x + 2
Answer: I think it’s f(x)=2x+2
Step-by-step explanation:
Help me out please I need help
Cliff needs 6 meters of wood for a building project. He already has 3
meters of wood.
Approximately how many feet of wood does Cliff need? (One meter
is approximately 3.3 feet.)
1 foot
3 feet
6 feet
10 feet
letter B 3 feet
Step-by-step explanation:
he needs three more to get 6 meters of wood
Tell whether the sum is positive, negative, or zero without adding them.
-8 + 20
Answer:
The sum is positive.
Step-by-step explanation:
The 20 is a far greater value than -8, so no matter what, when you add them the sum will be positive. Though this would not be the same were the -8 greater than -20.
Hope this helps!
A scuba diver is 12 meters below sea level. If the diver descends 39 meters further, what integer represents the scuba diver’s new elevation relative to sea level?
I think the answer is -51
whats 62.7×2.45......?
Answer:
153.615
Step-by-step explanation:
62.7 × 2.45=153.615
Round 34,138 to the nearest thousand??
Answer:
34,138 to the nearest thousand is 34,000!
Step-by-step explanation:
Hope this helps! Good luck! <3
Answer:
0
Step-by-step explanation:
Emiko makes shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying a scarves what do the parts of the expression 48s represents
The expression 48s represents the cost of the scarves.
Given
Emiko makes Shibori scarves and sells them for 48 each on a website for handmade goods the expression 48s represents the total price of buying scarves.
Let s represent the price of the scarves.
The cost of each scarves is 48.
Therefore,
The cost of scarves = Number of scarves × cost of each scarves.
The cost of scarves = s × 48
The cost of scarves = 48s
Hence, the expression 48s represents the cost of the scarves.
To know more about Expression click the link given below.
https://brainly.com/question/18371860
Answer:In the expression 48s ,represents the number of scarves and 48 represents the price per scarf
Step-by-step explanation:
in quadrilateral abcd below,
Answer: where is the quadrilateral
Step-by-step explanation:
Identify next 3 numbers in this sequence 2,6,3,9,6,18,15
diride 660cm in the ratio of 5:6
Answer:
Thus, the measure 660 cm is divided into 300 + 360 in the ratio of 5:6
Step-by-step explanation:
Equations
We are required to divide 660 cm in the ratio 5:6, or 5/6.
Let's call:
x = first part of 660
660 - x = second part of 660
The ratio between them is 5/6.
[tex]\displaystyle \frac{x}{660-x}=\frac{5}{6}[/tex]
The above equation will result in x as the smaller part of 660.
Multiply by (660-x)*6 to eliminate denominators:
[tex]\displaystyle (660-x)*6\cdot\frac{x}{660-x}=(660-x)*6\cdot\frac{5}{6}[/tex]
Operating:
[tex]6x=(660-x)*5[/tex]
[tex]6x=3300-5x[/tex]
Simplifying:
[tex]6x+5x=3300[/tex]
[tex]11x=3300[/tex]
Solving:
[tex]\displaystyle x=\frac{3300}{11}=300[/tex]
The other part is 660 - 300 = 360
Thus, the measure 660 cm is divided into 300 + 360 in the ratio of 5:6
Salena needs to purchase 9 skirts for a new job. her friend, Jamie goes with her each of the skirts costs $41. Salena says that she can find the total cost by multiplying 9 and 4 and adding that to product of 9 and 1. Jamie disagrees and says that she needs to find the product of 9 and 40 and add that to the product of 9 and 1. Who is correct and why?
Answer:
Jamie is correct. This is because 41 is a combination of 40 and 1. Salena thinks that the 4 is just a 4, however, the 4 is in the tens place, so the 41 without the 1 is 40. The answer to this 41 times 9 is 369. Not 45.
Step-by-step explanation:
Each skirt is $41
Salena needs 9
(9*40) + (9*1)
360 + 9
$369
what is 10x plus 50 - 2 divided by 6 + 100 times 8 - -2.
Answer: the answer is -947 hope this helped.
Step-by-step explanation:
6. The store paid $2.50 for a book and sold it for $5.25. What is the profit as a percent?
A rope is 12 meters long. You cut off 15/6 of the rope. How much is left?
Can you please add a step by step
Answer:
4.8
Step-by-step explanation:
15/6 is 2.5 whitch when divided by 12 is 4.8 so 12 divided by 2.5 is 4.8
Answer:
4.8 meters
Step-by-step explanation:
[tex]\frac{15}{6} = 2.5[/tex] 12 ÷ 2.5 = 4.8 metersI hope this helps!
Can someone please help me I need help and I can’t understand this plsssss
step 1. Multiply the variable x with 13 .
step 2. Add 2 to it .
Solution (b) :Step 1 : Subtract 2 from both sides : 13x + 2 - 2 = 41 - 2 = 39
Step 2 : Divide both the sides by 13 : 13x ÷ 13 = 39 ÷ 13 = 3
x = 3
Solution (2) :Solution (a) :Step 1. Subtract 3 from the variable .
Step 2. Divide the result by 5 .
Solution (b) :[tex]Step \: 1. \: add\: 3 \: to \: both \: the \: sides : \frac{x - 3}{5} + 3 = - 1 + 3
[/tex]
Step 2 : Multiply both the sides by 5 : 5 × 1/5x = 5 × -2/5
x = -2
Solve for x for the following pls!
1) 7+3x+1=4x+5
2) 8+2x+18=x+19
3) 6+2x+13=x+26
would appreciate it sm
Answer:
1.x=3
2. x= -7
3. x=7
Step-by-step explanation:
What’s the difference between m=change in y and change in x and m =y2-y1and x2-x1
it's the same thing
[tex]slope = \frac{Δy}{Δx} or \frac{change \: in \: y}{change \: in \: x} = \frac{y2 - y1}{x2 - x1} = \frac{rise}{run} [/tex]
Shen is on the swim team. Each week he swims a total of 5000 meters. How many kilometers does he swim each week?
Be sure to include the correct unit in your answer.
Answer:
5 km
Step-by-step explanation:
to convert m to km you have to divide by 1000.
5000/1000=5
hope this helps!
guys what is 265 divided by 53
Answer:
5
Step-by-step explanation:
265/53= 5
Answer:
265÷53=5
Step-by-step explanation:
just get a calculator
Please help me with all the answers please say like 1: the answer 2: the answer like that thank you so much
what does they y represent in the equation y=mx+b
Answer:
The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Step-by-step explanation:
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.
BI
Challenge 2
A: Can you find the
area of the circle?
r=x +1
B: Can you find the
circumference of
the circle?
Answer:
Area of the circle = pi * r^2 = pi * (x+1) ^ 2
Circumference of the circle = 2* pi * r = 2*pi*(x+1)
I don't understand with this question, can you help me with this pls?
Answer:
By moving the decimal at the end of the number to the correct amount of places for x 10 you move it once to the right for x 100 you move it right twice.
Step-by-step explanation:
How do you find what p is?
Answer:
p > -3
Step-by-step explanation:
This is an alternating p-series. It is absolutely convergent if│an│converges. 1 / nᵖ⁺³ converges if the exponent is greater than 1.
p + 3 > 1
p > -2
The series is conditionally convergent if │an│diverges. 1 / nᵖ⁺³ diverges if the exponent is greater than 0 and less than or equal to 1.
0 < p + 3 ≤ 1
-3 < p ≤ -2
Combining these two, we get p > -3.
People living in a society where one person rules by force have which type of government?
Answer:
An autocracy is a government structure in which the ultimate political authority is concentrated in one person's hands.
Hope this helps please give me brainliest!
God bless!
An autocracy.
An autocracy is a system of government in which a supreme political power is concentrated in the hands of one person.