A hand consists of 3 cards from a well-shuffled deck of 52 cards.
A. Find the number of possible 3-card poker hands.
B. A black flush is a 3-card hand consisting all red cards. Find the number of possible red flushes.
C. Find the probability of being dealt a black flush
A. To find the number of possible 3-card poker hands, we need to determine the number of ways to choose 3 cards out of a deck of 52 cards, which can be calculated using combinations. The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen.
In this case, we have n = 52 (the total number of cards in the deck) and r = 3 (the number of cards being chosen for the hand). So, the number of possible 3-card poker hands is C(52, 3) = 52! / (3!(52-3)!) = 22,100.
B. A black flush is a 3-card hand consisting of all red cards. Since there are 26 red cards (13 hearts and 13 diamonds) in the deck of 52 cards, we need to determine the number of ways to choose 3 red cards. Using the combinations formula, C(26, 3) = 26! / (3!(26-3)!) = 2,600.
C. To find the probability of being dealt a black flush, we need to divide the number of red flushes (2,600) by the total number of 3-card poker hands (22,100). So, the probability is 2,600 / 22,100 = 0.1176, or 11.76%.