3 cards are drawn simultaneously at random from a standard deck.
Find the probability that all the cards are hearts.
what is (13/52)(12/51)(11/50) = ?
To find the probability that all three cards drawn are hearts, we first need to find the total number of possible outcomes.
A standard deck has 52 cards, with 13 hearts.
The number of ways to choose 3 cards from a set of 52 can be calculated using the combinations formula:
C(52, 3) = 52! / (3!(52-3)!) = 22,100
Next, we need to determine the number of favorable outcomes, which is the number of ways to choose 3 hearts from the 13 available.
C(13, 3) = 13! / (3!(13-3)!) = 286
Finally, we can calculate the probability:
P(all cards are hearts) = favorable outcomes / total outcomes
= 286 / 22,100
≈ 0.0129 (rounded to four decimal places) or approximately 1.29%.
So, the probability is approximately 1.29% that all three cards drawn are hearts.