# Answer to Question #15831 in Statistics and Probability for Amie

Question #15831

If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a spade or Queen? Your answer must be accurate to three decimal places.

Expert's answer

There are 13 spades in a deck, so the probability to choose some spade is

P(spade) = 13/52 = 1/4.

There are 4 queens in a deck, so the probability to choose a queen is

P(queen) = 4/52 = 1/13.

The probability to choose the queen of spades is

P(queen of spades) = 1/52.

Therefore,

P(spade or queen) = P(spade) + P(queen) - P(queen of spades) = 1/4 + 1/13 - 1/52 = 4/13 ≈ 0.308.

So, the probability that the card you select is a spade or Queen is about .308.

P(spade) = 13/52 = 1/4.

There are 4 queens in a deck, so the probability to choose a queen is

P(queen) = 4/52 = 1/13.

The probability to choose the queen of spades is

P(queen of spades) = 1/52.

Therefore,

P(spade or queen) = P(spade) + P(queen) - P(queen of spades) = 1/4 + 1/13 - 1/52 = 4/13 ≈ 0.308.

So, the probability that the card you select is a spade or Queen is about .308.

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