Question

A bag contains 5 red and 7 black balls. A ball is drawn at random from the bag, the color is noted and the ball is replaced. A second ball is then drawn. Find the probability that the first ball is red and the second is black.

Answer 1

Answer: 35/144

Work Shown:

A = probability that 1st is red

A = (5 red)/(5 red + 7 black)

A = (5 red)/(12 total)

A = 5/12

B = probability that 2nd is black, previous ball was replaced

B = (7 black)/(12 total)

B = 7/12

C = probability that events A and B happen

C = A*B

C = (5/12)*(7/12)

C = (5*7)/(12*12)

C = 35/144