. 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.

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

Step-by-step 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

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get