# math

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.

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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)

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oobleck

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