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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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