SOLUTION: Three cards are selected at random from a standard deck of 52 playing cards. Determine the probability that all three cards are: a) Hearts b) Black c) Aces d)Face cards

Question 1117768: Three cards are selected at random from a standard deck of 52 playing cards. Determine the probability that all three cards are:
a)
Hearts
b)
Black
c)
Aces
d)Face cards
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

There are 13 hearts in a deck of 52 standard playing cards.

There are 13 ways to draw a heart from a full deck of 52, so the probability of a heart on the first draw is

. Once you have drawn the first heart, then there are only 12 hearts left in a deck of 51 cards, so

, and for the third card,

. Since these are three independent events, the probability of all three occurring is the product of the three individual probabilities. You can do your own arithmetic.

The other problems are solved exactly the same way. In a standard deck, 26 out of 52 are black cards, 4 out of 52 are Aces, and 12 out of 52 are face cards.

John

My calculator said it, I believe it, that settles it

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