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Chapter 6: Q. 107 (page 431)

Cranky mower To start her old lawn 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.

b. Find the probability that it takes her more than 6 pulls to start the mower.

Short Answer

Expert verified

(a)Thus, the required probability is 0.128

(b)Thus, the required probability is 0.24

Step by step solution

01

Part (a) Step 1: Given Information

Probability of success (p)=20%=0.20

Formula used:

The formula to compute the geometric distribution is:

P(X=x)=(1-p)x-1p

02

Part (a) Step 2: Simplificaiton

Consider, X be the random variable that follows the geometric distribution.

P(X=3)=(1-0.20){3-1}(0.20)=0.128

Thus, the required probability is 0.128.

03

Part (b) Step 1: Given information

Probability of success(p)=20percent

04

Part (b)  Step 2: Calculation

The probability that it will take more than 6 pulls can be calculated as:

P(X>6)=1-P(X鈮�6)=1-[P(X=1)+P(X=2)+鈥�.+P(X=6)]=1-[0.22+0.17+0.13+0.10+0.08+0.06]=0.24

Thus, the required probability is 0.24

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