Four cards from a standard deck of playing cards are randomly dealt to you. Find the probability that you are dealt exactly 3 aces.
To find the probability of being dealt exactly 3 aces, we need to calculate the number of favorable outcomes and the total number of possible outcomes.
First, let's determine the number of ways we can be dealt exactly 3 aces:
Since there are 4 aces in a standard deck, we can choose 3 aces out of 4 in C(4, 3) = 4 ways.
Once we have selected the 3 aces, there are 48 remaining cards in the deck. We need to choose an additional card that is not an ace, which can be done in C(48, 1) = 48 ways.
Therefore, the number of favorable outcomes is 4 * 48 = 192.
Next, let's calculate the total number of possible outcomes:
In a standard deck, there are 52 cards. We need to choose 4 cards out of the 52, which can be done in C(52, 4) = 270,725 ways.
Therefore, the probability of being dealt exactly 3 aces is given by:
P(3 aces) = (number of favorable outcomes) / (total number of possible outcomes)
P(3 aces) = 192 / 270,725 ≈ 0.00071
So, the probability of being dealt exactly 3 aces is approximately 0.00071 or 0.071%.