Edward S.

Probability

1 year, 1 month ago

If it is assumed that all $\left(\begin{array}{c}52 \\ 5\end{array}\right)$ poker hands are equally likely, what is the probability of being dealt
(a) a flush? (A hand is said to be a flush if all 5 cards are of the same suit.
(b) one pair? (This occurs when the cards have denominations $a, a, b, c, d,$ where $a, b, c,$ and $d$ are all distinct.
(c) two pairs? (This occurs when the cards have denominations $a, a, b, b, c,$ where $a, b,$ and $c$ are all distinct.)
(d) three of a kind? (This occurs when the cards have denominations $a, a, a, b, c,$ where $a, b$ and $c$ are all distinct.)
(e) four of a kind? (This occurs when the cards have denominations $a, a, a, a, b .)$