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 diamond or 5?Write your answer as a simplified fraction.
Question
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 diamond or 5?Write your answer as a simplified fraction.
Solution
To solve this problem, we need to consider two things: the number of diamonds in a deck and the number of 5's in a deck.
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There are 13 diamonds in a deck of 52 cards. So, the probability of drawing a diamond is 13/52 = 1/4.
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There are 4 fives in a deck (one for each suit: hearts, diamonds, clubs, spades). So, the probability of drawing a 5 is 4/52 = 1/13.
However, we have double-counted one card: the 5 of diamonds. This card is both a diamond and a 5, so it fits into both categories. We need to subtract the probability of drawing this one card from our total.
The probability of drawing the 5 of diamonds is 1/52.
So, the total probability of drawing a diamond or a 5 is (1/4 + 1/13 - 1/52).
To simplify this, we need to find a common denominator. The common denominator of 4, 13, and 52 is 52.
So, the total probability is (13/52 + 4/52 - 1/52) = 16/52 = 4/13.
So, the probability that the card you select is a diamond or a 5 is 4/13.
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