Final answer:
To find the probability of drawing at least one ace, calculate the complement (no aces drawn) and subtract from 1, multiplying the probabilities of not drawing an ace in each of the four draws.
Step-by-step explanation:
The question asks to calculate the probability of drawing at least one ace when four cards are drawn from a standard deck. The easiest way to calculate this is by finding the probability of the complementary event (drawing no aces) and subtracting it from 1. In a standard 52-card deck, there are 4 aces and 48 other cards.
The probability of not drawing an ace on the first draw is 48/52. Assuming we did not draw an ace, the probability of not drawing an ace on the second draw is 47/51. If we continue in this manner for four draws, we multiply these probabilities together:
- 1st card: 48/52
- 2nd card: 47/51
- 3rd card: 46/50
- 4th card: 45/49
We calculate the product of these probabilities to get the probability of drawing no aces in four draws:
P(no aces) = (48/52) × (47/51) × (46/50) × (45/49)
Now we find 1 - P(no aces) to get the probability of drawing at least one ace:
P(at least one ace) = 1 - P(no aces)
This value will give us the correct answer, which you can calculate to see which option it corresponds to (A, B, C, or D).