Question

You draw one card from a shuffled standard deck of cards (cards are in four suits —red diamonds, red hearts, black clubs, and black spades— and are numbered 2, 3, 4, 5, 6, 7, 8, 9, 10, j, q, k, a).
a.what is the probability of drawing a red card?
b.what is the probability of drawing a queen?
c.what is the probability of drawing a red queen?
d.what is the probability of drawing a queen given that you drew a face card (face cards are jacks, queens, and kings)

Answer 1

P(red card) = 1/2
P(queen) = 1/13
P(red queen) = 1/26
P(queen given face card) = 1/3

There are 26 red cards out of 52; the probability is 26/52 = 1/2.
There are 4 queens out of 52 cards; the probability is 4/52 = 1/13.
There are 2 red queens out of 52 cards; the probability is 2/52 = 1/26.
There are 12 face cards (4 jacks, 4 queens, and 4 kings).  Out of those, there are 4 queens.  The probability is 4/12 = 1/3.