Question

. A softball coach has 2 buckets of balls. One contains 15 new and 5 used balls. The second bucket contains 2 new and 8 used balls. The coach randomly selects a bucket and then randomly selects a ball from the bucket. a. Find the probability that the ball selected is new. b. Given that the coach selects a used ball, find the probability the ball is from the first bucket.

Answer 1

a) the probability that the ball selected is new is 0.475

b) the probability the ball is from the first bucket is 0.2381

Explanation:

A = the ball selected is new

B = the bucket selected by the coach is de first one.

P(A|B) = 15/(15+5)=0.75

P(A|B') = 2/(2+8)=0.2

P(B) = 0.5

a) by the total probability theorem

P(A) = P(A∩B) +P(A∩B') = P(A|B)*P(B) + P(A|B')*P(B') = 0.75*0.5+0.2*(1-0.5)=0.475

b) by the bayes rule

P(B|A')=P(A'|B)P(B)/P(A') = (1-0.75)*0.5/(1-0.475)=0.2381