Two cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find P(X = 2).
To find the probability of drawing 2 aces, we need to consider the total number of outcomes and the number of favorable outcomes.
Total number of outcomes:
When two cards are drawn from a well-shuffled deck of 52 playing cards, the total number of outcomes can be calculated using combination.
Since we are drawing two cards without replacement, the number of combinations can be calculated as:
52 choose 2 = C(52, 2) = 52! / (2!(52 - 2)!) = (52 * 51) / (2 * 1) = 1326.
Number of favorable outcomes:
To determine the number of favorable outcomes (drawing 2 aces), we need to consider that there are 4 aces in a deck of cards.
When the first card is drawn, there are 4 aces out of 52. After the first ace is drawn, there are 3 aces left out of the remaining 51 cards.
So, the number of combinations to draw 2 aces can be calculated as:
4 choose 2 = C(4, 2) = 4! / (2!(4 - 2)!) = (4 * 3) / (2 * 1) = 6.
Probability:
The probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes.
P(X = 2) = Number of favorable outcomes / Total number of outcomes
= 6 / 1326
So, P(X = 2) is approximately 0.0045 or 0.45%.