Using a standard 52-card deck, whats the probability of being dealt a pair of aces in a 5-card hand?
you want 2 out of the 4 aces
prob = C(4,2)/C(52,2)
= ....
To determine the probability of being dealt a pair of aces in a 5-card hand from a standard 52-card deck, we need to calculate the number of favorable outcomes (getting a pair of aces) and the total number of possible outcomes.
Step 1: Calculate the number of favorable outcomes (getting a pair of aces):
In a standard deck of 52 cards, there are 4 aces. To form a pair of aces, we need to choose 2 aces out of the 4 available.
C(4,2) = (4!)/(2!(4-2)!) = 6
There are 6 ways to choose a pair of aces.
Step 2: Calculate the total number of possible outcomes:
We need to calculate the number of possible 5-card combinations that can be formed from a 52-card deck.
C(52,5) = (52!)/(5!(52-5)!) = 2,598,960
There are 2,598,960 different 5-card combinations possible.
Step 3: Calculate the probability:
The probability is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = favorable outcomes / total outcomes
Probability = 6 / 2,598,960
Simplifying the fraction, we get:
Probability = 1 / 433,160
Therefore, the probability of being dealt a pair of aces in a 5-card hand from a standard 52-card deck is approximately 1 in 433,160.