Box I contains 1 red ball and 2 white balls. Box Il contains 2 red balls and 1 white ball. One ball is drawn randomly from box I and transferred to box II. Then, a ball is drawn randomly from box II and it is red. What is the probability that the transferred ball was white?

Box I contains 1 red ball and 2 white balls. Box Il contains 2 red balls and 1 white ball. One ball is drawn randomly from box I and transferred to box II. Then, a ball is drawn randomly from box II and it is red. What is the probability that the transferred ball was white?

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

Box I contains 1 red ball and 2 white balls. Box II contains 2 red balls and 1 white ball. One ball is
drawn randomly from box I and transferred to box II.
Then, a ball is drawn randomly from box II and it is red. What is the probability that the
transferred ball was white?

Expert Solution

Step 1

Let us define some events

A : transferred ball is white

B : transferred ball is red.

E : ball from box II is red.

From given information,

P(A) = 2/3, P(B) = 1/3

P(E|A) = 2/(2+2) = 1/2

P(E|B) = 3/(3+1) = 3/4

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