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Chapter 6: Q. 97 (page 405)

Cranky mower To start her old mower, Rita has to pull a cord and hope for some luck. On any particular pull, the mower has a 20%chance of starting.

(a) Find the probability that it takes her exactly 3 pulls to start the mower. Show your work.

(b) Find the probability that it takes her more than 10 pulls to start the mower. Show your work.

Short Answer

Expert verified

a. The probability that it takes her exactly 3pulls to start the mower is 12.8%

b. The probability that it takes her more than 10pulls to start the mower is 10.74%

Step by step solution

01

Part (a) Step 1: Given Information 

Cranky mower chance of starting=20%

Find the probability for 3pulls =?

02

Part (a) Step 2: Explanation 

Given:

p=20%=0.20

The formula for geometric probability:

P(X=k)=qk-1p=(1-p)k-1p

Find the value for k=3:

P(X=3)=(1-0.20)3-1(0.20)=0.128=12.8%

Hence, the probability is12.8%

03

Part (b) Step 1: Given Information 

Cranky mower chance of starting=20%

Find the probability for 3pulls=?

04

Part (b) Step 2: Explanation 

Given:

p=20%=0.20

Geometric probability formula:

P(X=k)=qk-1p=(1-p)k-1p

Find the probability using the complement rule:

P(X>10)=1-P(X≤10)=1−P(X=1)−P(X=2)−…−P(X=10)=1−0.8926=0.1074=10.74%

Hence, the probability is10.74%

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