A bag contains 13 red balls and 11 white balls. Two balls are drawn without replacement. What is the probability that the second ball is red R, given that the first ball is white W?
A) Pr(R |
W) =
B) Pr(R |
W) =
C) Pr(R |
W) =
D) Pr(R |
W) =
E) Pr(R |
W) =

Question

A bag contains 13 red balls and 11 white balls. Two balls are drawn without replacement. What is the probability that the second ball is red R, given that the first ball is white W? ​
A) Pr(R | 
W) = 
B) Pr(R | 
W) = 
C) Pr(R | 
W) = 
D) Pr(R | 
W) = 
E) Pr(R | 
W) =

Quizplus · Accepted Answer

We need to use Bayes' theorem to solve this problem:
Pr(R | W) = (Pr(W | R) * Pr(R)) / Pr(W)
Pr(R) = 13/24 (probability of red ball)
Pr(W) = 11/24 (probability of white ball)
Pr(W | R) = 11/23 (probability of white ball given that the first ball was red)
Therefore, Pr(R | W) = (11/23 * 13/24) / (11/24) = 11/23

A Bag Contains 13 Red Balls and 11 White Balls