Question 183370: Two cards are drawn from an ordinary deck of 52 cards. Find the probability of each event, showing reasoning carefully.
a. two aces
b. two red cards
c. two red aces
d. two honor cards (A, K, Q, J, 10)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! I'll do the first two to get you started
a)
There are 4 ace cards out of 52 cards total. Once you select an ace card, then you will have 3 aces left out of 51 total.
P(two aces) = P(one ace AND one ace)
P(two aces) = P(ace)*P(ace)
P(two aces) = (4/52)*(3/51)
P(two aces) = (1/13)*(1/17)
P(two aces) = 1/221
P(two aces) = 0.0045
So the probability of drawing 2 ace cards is 0.0045 or 0.45%
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b)
There are 26 red cards (diamonds and hearts) out of 52 cards total. Once you select a red card, then you will have 25 cards left out of 51 total
P(two red cards) = P(one red card AND one red card)
P(two red cards) = P(red)*P(red)
P(two red cards) = (26/52)*(25/51)
P(two red cards) = (1/2)*(25/51)
P(two red cards) = 25/102
P(two red cards) = 0.245
So the probability of drawing 2 red cards is 0.245 or 24.5%
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