Two balls are drawn in succession out of a box containing 2 red and 5 white balls. Find the probability that at least 1 ball was red, given that the first ball was left parenthesis Upper A right parenthesis Replaced before the second draw. left parenthesis Upper B right parenthesis Not replaced before the second draw.

a. The event that at least 1 red ball is drawn is complementary to the event that no red ball is drawn:

P (at least 1 red) = 1 - P (no red) = 1 - P (2 white)

The ball is replaced upon being drawn, so P (white) = 5/7 for each draw, so

P (2 white) = P (white) * P (white) = (5/7) ^2 = 25/49

Then

P (at least 1 red) = 1 - 25/49 = 24/49

b. The probability of drawing a white ball first remains the same, 5/7. Without replacement, the probability of drawing a second white ball is 4/6 = 2/3. Then

P (at least 1 red) = (5/7) * (2/3) = 10/21