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A box has 12 red cards and 12 black cards. Another box has 24 red cards and 24 black cards. You want to draw two cards at random from one of the two boxes, which box has a higher probability of getting cards of same colour and why?
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Answer Posted / Kiran
The box with 24 red cards and 24 black cards has a higher probability of drawing two cards of the same color compared to the box with 12 red cards and 12 black cards. This is because there are more combinations of drawing two cards of the same color in the larger box due to the larger number of repetitions of each color.nnFor the smaller box, there are C(12,2) = 66 possible combinations of drawing two cards, and only 12 of these combinations involve two red cards (C(12,2) / 66 ≈ 0.1818).nnFor the larger box, there are C(24,2) = 296 possible combinations of drawing two cards, and 24*24/296 ≈ 23.85 of these combinations involve two red cards (C(24,2) / 296 ≈ 0.0797).nnHence, the larger box has a higher probability of drawing two cards of the same color.
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