Finite math question

Question

Urn 1 contains 8 red and 2 white balls. Urn 2 contains 7 red and 2 white balls a ball is drawn from urn 1 and placed in urn 2 then a ball is drawn from urn 2 if the ball drawn from urn 2 is red what is the probability that the ball drawn from urn 1 was red

Answer 1

Sample space:

 

R R = .8 * . 8 = .64

R W = .8 * . 2 = .16

W R = .2 * .7 = .14

W W = .2 * .3 = .06

 

Event A = red from urn 1....P(A) = .8

Event B = red from urn 2....p(B) = .78

P(A ∩ B) = .64  

P(A|B) = P(A ∩ B)/P(B) = .64/.78 = .820513