. 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

3-4

step-by-step explanation:

the answer is 3-4 because both 45 and 60 has a multiple of 15.

45/3=15

60/4=15

therefore the odds against selecting a red is 4-3