EBK PRACTICE OF STAT.F/AP EXAM,UPDATED
EBK PRACTICE OF STAT.F/AP EXAM,UPDATED
6th Edition
ISBN: 9781319287573
Author: Starnes
Publisher: MPS PUB
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Question
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Chapter 5.3, Problem 87E

(a)

To determine

Probability for the person contributed to the charity.

(a)

Expert Solution
Check Mark

Answer to Problem 87E

Probability that the person contributed to the charity is 0.2240.

Explanation of Solution

Given information:

Figure showing probabilities for a charity by potential donors:

  EBK PRACTICE OF STAT.F/AP EXAM,UPDATED, Chapter 5.3, Problem 87E , additional homework tip  1

According to multiplication rule for independent events,

  P(AandBandC)=P(ABC)=P(A)×P(B)×P(C)

According to the addition rule for mutually exclusive events:

  P(ABC)=P(AorBorC)=P(A)+P(B)+P(C)

Let

R: Recent donor

P: Past donor

N: New prospect

PL: Pledge to contribute

C: Contributor

Now,

For recent donors:

Probability for recent donor,

  P(R)=0.5

Probability for recent donor pledge to contribute,

  P(PL)=0.4

Probability for recent donor makes contribution,

  P(C)=0.8

For past donors:

Probability for past donor,

  P(P)=0.3

Probability for past donor pledge to contribute,

  P(PL)=0.3

Probability for past donor makes contribution,

  P(C)=0.6

For new prospects:

Probability for new prospect,

  P(N)=0.2

Probability for new prospect pledge to contribute,

  P(PL)=0.1

Probability for new prospect makes contribution,

  P(C)=0.5

Now,

Since each person cannot become all three types of contributor,

Apply multiplication rule for each of the above three cases separately:

For recent donors:

  P(RPLC)=P(R)×P(PL)×P(C)=0.5×0.4×0.8=0.1600

For past donors:

  P(PPLC)=P(P)×P(PL)×P(C)=0.3×0.3×0.6=0.0540

For new prospect:

  P(NPLC)=P(N)×P(PL)×P(C)=0.2×0.1×0.5=0.0100

To get the probability for contributor,

Apply the addition rule for mutually exclusive events:

  P(C)=P(RPLC)+P(PPLC)+P(NPLC)=0.1600+0.0540+0.0100=0.2240

Thus,

The probability for the randomly selected person contributes to the charity is 0.2240.

(b)

To determine

Probability for the person contributed is a recent donor.

(b)

Expert Solution
Check Mark

Answer to Problem 87E

Probability that the person contributed is a recent donor is approx. 0.7143.

Explanation of Solution

Given information:

Figure showing probabilities for a charity by potential donors:

  EBK PRACTICE OF STAT.F/AP EXAM,UPDATED, Chapter 5.3, Problem 87E , additional homework tip  2

Conditional probability definition:

  P(A|B)=P(AB)P(B)

From Part (a),

We have

Probability for the person contributes to charity,

  P(C)=0.2240

Probability for recent donor and pledged to contribute and contributor,

  P(RPLC)=0.1600

It is understood that

Recent donor who contributed was pledged to contribute.

Thus,

  P(RPLC)=P(RC)=0.1600

Apply the conditional probability:

  P(R|C)=P(RC)P(C)=0.16000.22400.7143

Thus,

The conditional probability for the person contributed is a recent donor is approx. 0.7143.

Chapter 5 Solutions

EBK PRACTICE OF STAT.F/AP EXAM,UPDATED

Ch. 5.1 - Prob. 11ECh. 5.1 - Prob. 12ECh. 5.1 - Prob. 13ECh. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Prob. 19ECh. 5.1 - Prob. 20ECh. 5.1 - Prob. 21ECh. 5.1 - Prob. 22ECh. 5.1 - Prob. 23ECh. 5.1 - Prob. 24ECh. 5.1 - Prob. 25ECh. 5.1 - Prob. 26ECh. 5.1 - Prob. 27ECh. 5.1 - Prob. 28ECh. 5.1 - Prob. 29ECh. 5.1 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - Prob. 33ECh. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - Prob. 36ECh. 5.2 - Prob. 37ECh. 5.2 - Prob. 38ECh. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.2 - Prob. 47ECh. 5.2 - Prob. 48ECh. 5.2 - Prob. 49ECh. 5.2 - Prob. 50ECh. 5.2 - Prob. 51ECh. 5.2 - Prob. 52ECh. 5.2 - Prob. 53ECh. 5.2 - Prob. 54ECh. 5.2 - Prob. 55ECh. 5.2 - Prob. 56ECh. 5.2 - Prob. 57ECh. 5.2 - Prob. 58ECh. 5.2 - Prob. 59ECh. 5.2 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - Prob. 62ECh. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Prob. 65ECh. 5.3 - Prob. 66ECh. 5.3 - Prob. 67ECh. 5.3 - Prob. 68ECh. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Prob. 80ECh. 5.3 - Prob. 81ECh. 5.3 - Prob. 82ECh. 5.3 - Prob. 83ECh. 5.3 - Prob. 84ECh. 5.3 - Prob. 85ECh. 5.3 - Prob. 86ECh. 5.3 - Prob. 87ECh. 5.3 - Prob. 88ECh. 5.3 - Prob. 89ECh. 5.3 - Prob. 90ECh. 5.3 - Prob. 91ECh. 5.3 - Prob. 92ECh. 5.3 - Prob. 93ECh. 5.3 - Prob. 94ECh. 5.3 - Prob. 95ECh. 5.3 - Prob. 96ECh. 5.3 - Prob. 97ECh. 5.3 - Prob. 98ECh. 5.3 - Prob. 99ECh. 5.3 - Prob. 100ECh. 5.3 - Prob. 101ECh. 5.3 - Prob. 102ECh. 5.3 - Prob. 103ECh. 5.3 - Prob. 104ECh. 5.3 - Prob. 105ECh. 5.3 - Prob. 106ECh. 5.3 - Prob. 107ECh. 5.3 - Prob. 108ECh. 5 - Prob. R5.1RECh. 5 - Prob. R5.2RECh. 5 - Prob. R5.3RECh. 5 - Prob. R5.4RECh. 5 - Prob. R5.5RECh. 5 - Prob. R5.6RECh. 5 - Prob. R5.7RECh. 5 - Prob. R5.8RECh. 5 - Prob. T5.1SPTCh. 5 - Prob. T5.2SPTCh. 5 - Prob. T5.3SPTCh. 5 - Prob. T5.4SPTCh. 5 - Prob. T5.5SPTCh. 5 - Prob. T5.6SPTCh. 5 - Prob. T5.7SPTCh. 5 - Prob. T5.8SPTCh. 5 - Prob. T5.9SPTCh. 5 - Prob. T5.10SPTCh. 5 - Prob. T5.11SPTCh. 5 - Prob. T5.12SPTCh. 5 - Prob. T5.13SPTCh. 5 - Prob. T5.14SPT
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