CARD SELECTING QUESTION!!

Question

Consider selecting 13 cards randomly from a pack of 52 cards. What is the prob that those 13 cards contain exactly one king given that those 13 cards contain 2 queen.

Answer 1

P(hand with 13 cards contains 1 king| it contains 2 queens) =

P(hand with 13 cards contains 1 king and 2 queens)/P(hand with 13 cards contains 2 queens) =

Number of hands with 13 cards contains 1 king and 2 queens/Number of hands with 13 cards containing two queens =

(as there are 44 cards not queen or king and 48 cards not queen, and we need 10 and 11 of these, respectively)

C(4,1)C(4,2)C(44,10)/(C(4,2)C(48,11) =

4*6*2481256778/(6*22595200368) =

59550162672/135571202208 =

2849/6486 is approximately

0.4393