A bag contains 3 red and 5 black balls and two balls are drawn at random together. Which is the greater probability — that both drawn balls are red, or that both are black — and by how much?

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Accepted Answer

Both black is greater, by 1/4. Total ways = C(8,2) = 28. Both red = C(3,2)/28 = 3/28; both black = C(5,2)/28 = 10/28. So 'both black' is greater and the difference is 10/28 - 3/28 = 7/28 = 1/4.

A bag contains 3 red and 5 black balls and two balls are drawn at random together. Which is the greater probability — that both drawn balls are red, or that both are black — and by how much?

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