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Chapter 3: Q.3.9 (page 110)

You ask your neighbor to water a sickly plant while you are on vacation. Without water, it will die with probability .8; with water, it will die with probability .15. You are 90percent certain that your neighbor will remember to water the plant.

(a) What is the probability that the plant will be alive when you return?

(b) If the plant is dead upon your return, what is the probability that your neighbor forgot to water it?

Short Answer

Expert verified

a). The probability that the plant will be alive when you return is 0.785.

b). The probability that your neighbor forgot to water it islocalid="1650015942117" 0.3721.

Step by step solution

01

 Given Information (Part a) 

W-. the plants were watered

PD鈭�Wc=0.8

P(D鈭�W)=0.15

P(W)=0.9

02

Explanation (Part a)

Formula of total probability can be applied here (because W鈭�Wc=鈭�,PW鈭�Wc=1 ):

P(D)=PD鈭�WcPWc+P(D鈭�W)P(W)

Formula for complement 鈬�PWc=1-P(W)=0.1

Substitution of familiar probabilities:

P(D)=0.8路0.1+0.15路0.9=0.215

Now formula for complement applied again:

PDc=1-P(D)=1-0.215=0.785

03

Given Information (Part b)

W-. the plants were watered

D- the plants died

Given probabilities:

PD鈭�Wc=0.8P(D鈭�W)=0.15P(W)=0.9
04

Explanation (Part b)

The definition of conditional probability gives:

PWc鈭�D=PWc鈭�DP(D)andPD鈭�Wc路PWc=PWc鈭�D

Which can be fused into:

PWc鈭�D=PD鈭�Wc路PWcP(D)

In part a) we computed PWc=0.1,P(D)=0.215is stated in the beginning, therefore:

localid="1650015923077" PWc鈭�D=0.8路0.10.215=1643鈮�0.3721

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