Suppose 2 cards are drawen without replacement from an ordin

Suppose 2 cards are drawen without replacement from an ordinary deck of 52 cards. find the probability of the given results. a- both cards are black b- both cards are hearts. c-exactly 1 is a face card. d- at most 1 is an ace.

Solution

a)

There are 52C2 ways to choose ny 2 cards.

There are 26C2 ways to choose two balck cards.

Thus,

P(both black) = 26C2 / 52C2 = 0.245098039 [ANSWER]

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b)

There are 13C2 ways to choose two hearts.

P(both hearts) = 13C2 / 52C2 = 0.058823529 [ANSWER]

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c)

There are 12 ways to choose a face card, and 40 other ways to choose the other. Thus,

P = 12*40/ 52C2 = 0.36199095 [ANSWER]

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d)

There are 48C2 ways so that there are no aces.

There are 4*48 ways so that there is exactly 1 ace.

P(at most 1 ace) = (48C2 + 4*48)/(52C2) = 0.995475113 [ANSWER]