What is the probability that a randomly selected poker hand contains exactly 3 queens given that it contains atleast two queens?
Answers
Given : a randomly selected poker hands contains exactly 3 queens , given that it contains at least 2 queens
To Find : probability that a randomly selected poker hands contains exactly 3 queens, given that it contains at least 2 queens
Solution :
A poker hand has 5 cards
it contains exactly 2 queens
= ⁴C₂ * ⁴⁸C₃
= 6 * 17,296
= 1,03,776 ways
contains exactly 3 queens
= ⁴C₃* ⁴⁸C₂
= 4* 1,128
= 4512 Ways
contains exactly 4 queens
= ⁴C₄* ⁴⁸C₁
= 48 Ways
contains at least 2 queens = 1,03,776 + 4512 + 48 = 1,08,336 Ways
probability that a randomly selected poker hands contains exactly 3 queens, given that it contains at least 2 queens = 4512 / 1,08,336
= 94/2257
= 0.04165
probability that a randomly selected poker hands contains exactly 3 queens, given that it contains at least 2 queens = 94/2257
or 0.04165
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