Final answer:
The probability of being dealt a hand missing the hearts in a bridge game is calculated using combinations, expressed as C(39, 13) / C(52, 13), where C(n, k) is the number of combinations of n items taken k at a time.
Step-by-step explanation:
The question asks for the probability that a 13-card hand from a standard deck of 52 cards is missing an entire suit—in this case, hearts. A standard deck consists of four suits: clubs, diamonds, hearts, and spades, with 13 cards in each suit.
To calculate this probability, we need to consider that there are 39 cards that are not hearts in the deck (13 clubs, 13 diamonds, and 13 spades). A bridge hand consists of 13 cards, so the number of ways to select 13 cards that are not hearts is the number of combinations of 39 cards taken 13 at a time, which is denoted as C(39, 13).
The total number of possible hands is the number of combinations of 52 cards taken 13 at a time, denoted as C(52, 13).
Thus, the probability of being dealt a hand with no hearts is given by:
P(No Hearts) = C(39, 13) / C(52, 13)
Using the combination formula C(n, k) = n! / [k! * (n-k)!], where n is the total number of items, k is the number of items to choose, and '!' denotes factorial, we can plug in the numbers to calculate the probabilit