Buddy is a dog who loves to play catch. Unfortunately, he’s not very good, and the probability that he catches a ball is only 0.1. Let x be the number of tosses required until Buddy catches a ball. This would be a GEOMETRIC distribution. a) What is the probability that it will take exactly 2 tosses for Buddy to catch a ball? b) What is the probability that more than 3 tosses will be r

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Buddy is a dog who loves to play catch. Unfortunately, he’s not very good, and the probability that he catches a ball is only 0.1. Let x be the number of tosses required until Buddy catches a ball. This would be a GEOMETRIC distribution.

a) What is the probability that it will take exactly 2 tosses for Buddy to catch a ball?

b) What is the probability that more than 3 tosses will be required?

Expert Solution
Step 1

Let X be the number of tosses required until Buddy catches a ball.

The probability mass function for X is,

PX=k=(1-p)k-1p,       k=1,2,3....              =(1-0.1)k-10.1, k=1,2,3....              =0.9k-10.1,          k=1,2,3......

a)

The probability that it will take exactly 2 tosses for Buddy to catch a ball is,

PX=2=(1-0.1)2-10.1              =0.09

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