SOLUTION: suppose we draw a card from a shuffled set of 52 playing cards. what is the probability of drawing a queen, given that the card drawn is of suit Hearts?

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Question 1169086: suppose we draw a card from a shuffled set of 52 playing cards.
what is the probability of drawing a queen, given that the card drawn is of suit Hearts?
Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


Using the formal definition of conditional probability....

P(A|B) = P(A and B)/P(B)

we get

P(queen|hearts) = P(queen and hearts)/P(hearts) = (number of cards that are queens AND hearts)/(number of hearts) = 1/13.

Informally, "...given that the card is hearts" means the denominator of the probability fraction is only the number of hearts. Then the problem becomes finding the probability that when a heart is chosen it is a queen; of course since only 1 of the 13 hearts is a queen, the answer is 1/13.