SOLUTION: hey i will greatly appreciate it if you could help me with this probability question: Two cards are drawn from a deck of 52 playing cards. Find the probability of each of the fo

Question 157012: hey i will greatly appreciate it if you could help me with this probability question:
Two cards are drawn from a deck of 52 playing cards. Find the probability of each of the following events occuring:
a) Both cards are clubs
b) Both cards are red
c) Both cards are queens
d) Both cards are red queens

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
52 cards in the deck (not counting the joker).
4 suits with 13 cards each (ace through 10 + jack queen king)
26 red
4 queens
2 red queens
probability of drawing 2 clubs is (13/52) * (12/51)
probability of drawing 2 red cards is (26/52) * (25/51)
probability of drawing 2 queens is (4/52) * (3/51)
probability of drawing 2 red queens is (2/52) * (1/51).
here's how it works.
the probability of any event happening is the number of ways it can happen divided by the total number of ways anything can happen.
the probability of any 2 events happening is the probability of the first event happening times the probability of the second event happening.
with the cards, there are 13 clubs in the deck.
the probability of getting a club is 13 / 52 because there are 52 total cards in the deck.
once the club has been taken, there are 12 clubs left in the deck and 51 cards total, so the probability of a club being taken again is 12 / 51.
the probability of both events happening is the probability of the first event times the probability of the second event so the answer is (13/52) * (12/51).

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