What is the likelihood that the fourth ball drawn from the bag is the third red ball in the sequence, given that three red and five yellow ping pong balls are initially placed in the bag, and the balls are drawn one by one without replacement until none remain in the bag?

What is the likelihood that the fourth ball drawn from the bag is the third red ball in the sequence, given that three red and five yellow ping pong balls are initially placed in the bag, and the balls are drawn one by one without replacement until none remain in the bag?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

Expert Solution

Step 1: Probability obtained.

We have

3 red (R) balls and 5 yellow (Y) balls in the bag.Balls are drawn one by one without replacement

Third ball is red. The sequence may be

RRR, RYR, YRR, YYR . The probabilities are

P(RRR) = $3 over 8 space 2 over 7 space 1 over 6 space equals 6 over 336$

P(RYR) = $fraction numerator 3 space over denominator 8 space end fraction space 5 over 7 space 2 over 6 space equals 30 over 336$

P(YRR) = $5 over 8 space 3 over 7 space 2 over 6 space equals 30 over 336$

P(YYR) = $5 over 8 space 4 over 7 3 over 6 space equals space 60 over 336$

P(getting R in the third draw) = P(RRR)+P(RYR)+P(YRR)+P(YYR) = $fraction numerator 6 plus 30 plus 30 plus 60 over denominator 336 end fraction space equals 126 over 336 space equals 0.375$

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