Three cards are chosen at random from a standard 52-card deck. Find the probability that all three cards are hearts given that there are 13 hearts in the deck. Round to the nearest thousandth.
Is this 0.013?
Prob(3 hearts) = C(13,3)/C(52,3)
= 286/22100
= .0129
yes
To find the probability that all three cards are hearts, we need to determine the number of favorable outcomes (cases where all three cards are hearts) and the total number of possible outcomes.
The total number of possible outcomes is the number of ways we can choose 3 cards from the 52-card deck, which can be calculated using the combination formula:
C(n, r) = n! / (r!(n-r)!)
Here, n represents the total number of items (52 cards) and r represents the number of items to be chosen (3 cards).
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 we can choose 3 hearts from the 13 hearts in the deck. This can be calculated using the combination formula as well:
C(13, 3) = 13! / (3!(13-3)!) = 286
Finally, we can calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of Favorable Outcomes / Total Number of Possible Outcomes = 286 / 22,100 ≈ 0.01295
Rounding to the nearest thousandth, the probability that all three cards are hearts is approximately 0.013.
So no, the probability is not exactly 0.013, it is slightly less.