Question

Suppose that a single card is selected from a standard 52-card deck. Who at is the probability th at the card drawn is a club? Now suppose that a single card is drawn from a standard 52-deck card, but it is told that the card is black. What is the probability that the card drawn is a club

Answer 1

Step-by-step expA = number of black cards

B = number of picture cards (or face cards)

C = number of black picture cards

There are 26 black cards (spades and clubs), so A = 26.

There are 3 picture cards (Jack, Queen, King) in each suit. There are 4 suits (clubs, hearts, spades, diamonds). So there are 3*4 = 12 picture cards. This means B = 12

There are 2 suits which are black (spades and clubs) with 3 face cards per suit, so 2*3 = 6 cards which are both black cards and face cards. So C = 6

The number of cards that are either black cards or a face card, or both, is...

D = A+B-C

D = 26+12-6

D = 32

So there are 32 cards that are either black cards or a face card, or both

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This is out of 52 cards total, so

probability of selecting a black card or a picture card = D/52

probability of selecting a black card or a picture card = 32/52

probability of selecting a black card or a picture card = 8/13

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The final answer, as a fraction, is 8/13