question_answer 1)

A black and a red dice are rolled (a) Find the conditional probability of obtaing a sum greater than 9, given that the black die resulted in a 5. (b) Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.  

Answer:

n (S) = 36       (a) Let A = Event of getting sum greater than 9.             = {4, 6), (5, 5), (6, 4), (5, 6), (6, 5), (6, 6)}             and B = event of getting 5 on black die             = {(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}                                     Required conditional probability is                         (b)Let E = event of getting sum 8             = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}       and F = event of getting a number less than 4 on red die       = {(1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (6, 1), (1, 2), (2, 2), (3, 2), (4, 2), (5, 2), (5, 2), (1, 3), (2, 3), (3, 3), (4, 3), (5, 3), (6, 3)}             Now       Required conditional probability is