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.

P ( A ) = 20 12 ​ ⋅ 19 8 ​ + 20 8 ​ ⋅ 19 12 ​ = 20 ⋅ 19 12 ⋅ 8 ​ ⋅ 2 = 5 ⋅ 19 12 ⋅ 4 ​ = 95 48 ​

Answered by kate200468 | 2024-06-10

The probability that the two marbles drawn from the bottle are not the same color is 95 48 ​ . This is calculated by considering the two scenarios: drawing a red marble first and then a blue, or a blue marble first and then a red. The computations result in the same probability for both scenarios, which when added together gives the final probability.
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Answered by kate200468 | 2024-09-26