Two cards are drawn from a standard deck of 52 where the first card is NOT replaced before the second card is drawn. Find the probability that both cards are aces.
Two cards are drawn from a standard deck of 52 where the first card is NOT replaced before the second card is drawn. Find the probability that both cards are face cards (jack, queen, or king).
Probability that all events will occur is found by multiplying the probability of individual events.
Aces = 4/52 * 3/51 = ?
Faces = 12/52 * 11/51 = ?
To find the probability that both cards are aces, we need to determine the number of favorable outcomes (two aces) and the total number of possible outcomes.
First, let's determine the number of favorable outcomes. There are four aces in a standard deck, so for the first card, there are 4 aces out of 52 cards. After the first card is drawn, there are only 3 aces left in a deck of 51 cards. Therefore, the number of favorable outcomes is 4 * 3 = 12.
Next, let's determine the total number of possible outcomes. For the first card, there are 52 cards to choose from. After the first card is drawn, there are 51 cards left in the deck. Therefore, the total number of possible outcomes is 52 * 51 = 2,652.
Finally, we can divide the number of favorable outcomes by the total number of possible outcomes to find the probability. So, the probability of drawing two aces is 12 / 2,652 ≈ 0.0045.
Therefore, the probability that both cards are aces is approximately 0.0045.