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 red 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 red flush.
To find the number of possible 3-card poker hands, we need to choose 3 cards out of 52. This can be calculated using the combination formula:
Number of possible 3-card poker hands = C(52, 3) = 52! / (3! * (52-3)!) = 22,100
To find the number of possible red flushes, we need to choose 3 cards out of the 26 red cards in the deck. Again, this can be calculated using the combination formula:
Number of possible red flushes = C(26, 3) = 26! / (3! * (26-3)!) = 2,600
To find the probability of being dealt a red flush, we need to divide the number of possible red flushes by the number of possible 3-card poker hands:
Probability of being dealt a red flush = Number of possible red flushes / Number of possible 3-card poker hands = 2,600 / 22,100 ≈ 0.1176 or 11.76%