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Days01234567Probability0.680.050.070.080.050.040.010.02

Working out Refer to Exercise 6. Consider the events A = works out at least once and B = works out less than 5 times per week.

(a) What outcomes makeup event A? What is P(A)?

(b) What outcomes make up event B? What is P(B)?

(c) What outcomes make up the event 鈥淎 and B鈥? What is P(A and B)? Why is this probability not equal to P(A) 路 P(B)?

Short Answer

Expert verified

a)The probability of P(A)isrole="math" localid="1649478583105" 0.32

b)the probability of P(B)is0.93

c)P(AandB)P(A)P(B)because the events are not independent.

Step by step solution

01

Part (a) Step 1: Given Information 

Given probability distribution is

Days01234567Probability0.680.050.070.080.050.040.010.02

02

Part (a) Step 2: Calculation 

Consider Aas the event that depicts the workout at least once.

The outcomes for the event Acan be written as:

Outcomes={1,2,3,4,5,6,7}

P(A)can be calculated as:

localid="1649992396909" P(A)=P(X=1)+P(X=2)+..+P(X=7)=0.05+0.08+..+0.02=0.32

03

Part (b) Step 1: Given Information 

Given probability distribution is

Days01234567Probability0.680.050.070.080.050.040.010.02

04

Part (b) Step 2: Calculation 

Consider Aas the event that depicts the workout less than 5times in a week.

The outcomes for the event localid="1649992417188" Bcan be written as:

Outcomes={0,1,2,3,4}

P(B)can be calculated as:

localid="1649992420222" P(B)=P(X=0)+P(X=1)+..+P(X=4)=0.68+0.05++0.05=0.93

05

Part (c) Step 1: Given Information 

Given probability distribution is

Days01234567Probability0.680.050.070.080.050.040.010.02

06

Part (c) Step 2: Calculation 

Using the data of the above parts, the outcomes for the event Aand Bcan be written as:

Outcomes={1,2,3,4}

P(Aand B)can be calculated as:

localid="1649992432843" P(AandB)=P(X=1)+P(X=2)+P(X=3)+P(X=4)=0.05+0.07+0.08+0.05=0.25

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Most popular questions from this chapter

7. Benford鈥檚 law Refer to Exercise 5. The first digit of a randomly chosen expense account claim follows Benford鈥檚 law. Consider the events A = first digit is 7 or greater and B = first digit is odd.

(a) What outcomes make up the event A? What is P(A)?

(b) What outcomes make up the event B? What is P(B)?

(c) What outcomes make up the event 鈥淎 or B鈥? What is P(A or B)? Why is this probability not equal to P(A) + P(B)?

A small ferry runs every half hour from one side of a large river to the other. The number of cars Xon a randomly chosen ferry trip has the probability distribution shown below. You can check that X=3.87and X=1.29.

(a) The cost for the ferry trip is $5. Make a graph of the probability distribution for the random variable M=money collected on a randomly selected ferry trip. Describe its shape.

(b) Find and interpret M.

(c) Compute and interpret M.

How well does it 铿乼? (3.2) Discuss what s, r2, and the residual plot tells you about this linear regression model.

Refer to Exercise 37. The ferry company鈥檚 expenses are $20per trip. Define the random variable Yto be the amount of profit (money collected minus expenses) made by the ferry company on a randomly selected trip. That is, Y=M20.

(a) How does the mean of Yrelate to the mean of M? Justify your answer. What is the practical importance of Y?

(b) How does the standard deviation of Yrelate to the standard deviation of M? Justify your answer. What is the practical importance of Y?

Suppose you roll a pair of fair, six-sided dice until you get doubles. Let T=the number of rolls it takes.

Find P(T=3). Interpret this result in context.

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