Question 1026636: One card is randomly selected from a deck of 52 cards. Find the probability of selecting a black card or a picture card?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Let
A = 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
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