Question

Two balls are chosen from an urn without replacement. 3 are black and 4 are white. Find a) the probability that both of the balls are the same color b) given that at least one of the balls is white, what is probability that the other ball is white?

Answer 1

a) P(both balls are of same color) = P(both are white) + P(both are black)

= 4/7 x 3/6 + 3/7 x 2/6

= 3/7

= 0.4286

b) Bayes' Theorem: P(A | B) = P(A & B)/P(B)

P(both are white | at least one ball is white) = P(both are white) / P(at least one ball is white)

= P(both are white) / (1 - P(both are black)

= (4/7 x 3/6)/(1 - 3/7 x 2/6)

= 1/3

= 0.3333