Question

What is the probability that a five-card poker hand contains at least one ace, where the probability is calculated based on:

A) Number of face cards
B) Number of suits in the deck
C) Total number of possible hands
D) Number of aces in the deck

Answer 1

The probability that a five-card poker hand contains at least one ace can be calculated using the formula for complementary probabilities.

Step-by-step explanation:

The probability that a five-card poker hand contains at least one ace can be calculated using the formula for complementary probabilities. To find the probability of an event occurring, we subtract the probability of its complement from 1.

A) The number of face cards in a deck is 12 (4 aces and 8 face cards).
B) The number of suits in a deck is 4.
C) The total number of possible poker hands is 2,598,960.
D) The number of aces in a deck is 4.

Using the formula:

P(at least one ace) = 1 - P(no aces)

P(no aces) = (48 C 5) / (52 C 5)

The probability of getting at least one ace is:

P(at least one ace) = 1 - [(48 C 5) / (52 C 5)]