Question

Compute the probability of randomly drawing a (5-card) Poker hand containing 2 Queens, another pair of cards (distinct from Queens), and a 5th card from another denomination.

Compute the probability of randomly drawing a (5-card) Poker hand containing 2 Queens, another pair of cards (distinct from Queens), and a 5th card from another denomination.

Answer 1

Total cards dealt = 5

Number of ways in which 5 cards can be dealt from a deck of 52 cards =

2 queens can be selected in ways

There are 12 numbers in the deck now other than the queen from which the second type of pair has to be selected

The second type of pair other than queen can be selected in ways

Of the second type, 2 cards can be selected in ways

After the queen and the second type of pair cards are removed, there remain 44 cards

The remaining 1 card has to be selected from the 44 cards in ways

Thus the required probability

= 0.0073

Required probability =

--------------------------------------------------------------------------------------------------------------------
If you are satisfied with the solution, kindly give a thumbs up.