Suppose that the balls in a large bucket of colored ping pong balls consist of 40%...

Suppose that the balls in a large bucket of colored ping pong balls consist of 40% red balls, 50% green balls, and 10% yellow balls. Suppose that 5% of the red balls are dented, 2% of the green balls are dented, and 1% of the yellow balls are dented. Assume that all the balls are equally likely to be selected on a random draw from the bucket.

A) The probability that a randomly selected ping pong ball is dented =

B) Suppose that a randomly selected ball drawn from the bucket is dented. Given that the ball is dented, then the probability that its color is green =

Solutions

Expert Solution

Define the following events

red=event that a randomly selected ball is red
green=event that a randomly selected ball is green
yellow=event that a randomly selected ball is yellow
dented=event that a randomly selected ball is dented

We have the following probabilities

The probability that a randomly selected ball is red is

P(red) = 0.40

The probability that a randomly selected ball is green is

P(green)=0.50

The probability that a randomly selected ball is yellow is

P(yellow)=0.10

5% of the red balls are dented

The conditional probability of a ball being dented, given that it is red is

2% of the green balls are dented

The conditional probability of a ball being dented, given that it is green is

1% of the yellow balls are dented

The conditional probability of a ball being dented, given that it is yellow is

a) The probability that a randomly selected ping pong ball is dented is

ans: The probability that a randomly selected ping pong ball is dented is 0.031

b) Given that a randomly selected ball is dented, then the probability that its color is green is

ans: Given that the ball is dented, then the probability that its color is green = 0.3226

orchestra answered 1 year ago

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