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Find the conditional probability that a randomly selected poker hands contains exactly 3aces, given that it contains at least 2 aces? |
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Answer» Given : a randomly selected poker hands contains exactly 3 aces, given that it contains at LEAST 2 aces To Find : probability that a randomly selected poker hands contains exactly 3 aces, given that it contains at least 2 aces Solution : A poker hand has 5 cards it contains exactly 2 aces = ⁴C₂ * ⁴⁸C₃ = 6 * 17,296 = 1,03,776 ways contains exactly 3 aces = ⁴C₃* ⁴⁸C₂ = 4* 1,128 = 4512 Ways contains exactly 4 aces = ⁴C₄* ⁴⁸C₁ = 48 Ways contains at least 2 aces = 1,03,776 + 4512 + 48 = 1,08,336 Ways probability that a randomly selected poker hands contains exactly 3 aces, given that it contains at least 2 aces = 4512 / 1,08,336 = 94/2257 = 0.04165 probability that a randomly selected poker hands contains exactly 3 aces, given that it contains at least 2 aces = 94/2257 or 0.04165 Learn More: A pair of fair dice is thrown independently FOUR times. The probability ... A pair of dice is thrown together till a sum of 4 or 8 is obtained. The ... |
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