A bridge hand consists of 13 cards dealt from a standard 52 card deck what is the probability of being dealt exactly five spades?

Answer 1

To calculate the probability of being dealt exactly five spades in a 13-card bridge hand, we can use the hypergeometric distribution. The number of ways to choose 5 spades from the 13 available is given by ( \binom{13}{5} ), and the number of ways to choose the remaining 8 cards from the 39 non-spades is ( \binom{39}{8} ). The total number of ways to choose any 13 cards from the 52-card deck is ( \binom{52}{13} ). Thus, the probability is given by:

[ P(X = 5) = \frac{\binom{13}{5} \cdot \binom{39}{8}}{\binom{52}{13}}. ]