The experiment of choosing 5 cards from 52 and 52C5 equally likely outcomes. Of those, there are 13C5 combinations that contain 5(of the 13) hearts.
P(all hearts) = 13C5/52C5 = 1,287/2,598,960 = 0.000495
Five cards are drawn at random from a standard deck. Find the probability that exactly 2 are hearts.
P(2 hearts and 3 non-hearts) = 13C2 • 39C3/52C5 = 75 • 9139/2,598,960 = 0.274
Three marbles are picked at random from a bag containing 4 red marbles and 5 white marbles. Match each event with its probability.
a. All three marbles are red 4C3 • 5C0/9C3
b. Exactly 2 marbles are red 4C2 • 5C1/9C3
c. Exactly 1 marble is red 4C1 • 5C2/9C3
d. No marble is red 4C0 • 5C3/9C3
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