A bottle contains 12 red marbles and 8 blue marbles. A marble is chosen at random and not replaced. Then, a second marble is chosen at random. Determine the probability that the two marbles are not the same color. Determine the probability that at least one of the marbles is red.

Answer 1

20 marbles in all
P1(red,blue) = 12/20 * 8/19
P2(blue,red) = 8/20 * 12/19
so, P(different) = P1+P2 = 48/95
Note that
P1(red,red) = 12/20 * 11/19
P2(blue,blue) = 8/20 * 7/19
P(not same) = 1 - (P1+P2) = 48/95

P(at least 1 red) = 1 - P(blue,blue) = 81/95
Check to see that this is also P(not same) + P(red,red)