A card is drawn randomly from an ordinary deck of playing cards that has 52 cards. What is the probability that you will get a three or diamond? Round your answer to two decimal places.
Question
A card is drawn randomly from an ordinary deck of playing cards that has 52 cards. What is the probability that you will get a three or diamond? Round your answer to two decimal places.
Solution
To solve this problem, we need to understand that there are 4 threes and 13 diamonds in a deck of 52 cards. However, one of the threes is a diamond, and we can't count it twice.
Step 1: Calculate the probability of drawing a three. There are 4 threes in a deck of 52 cards. So, the probability is 4/52 = 0.0769.
Step 2: Calculate the probability of drawing a diamond. There are 13 diamonds in a deck of 52 cards. So, the probability is 13/52 = 0.25.
Step 3: Add the two probabilities together. However, we have to subtract the probability of drawing a three of diamonds because we have counted it twice. The probability of drawing a three of diamonds is 1/52 = 0.0192.
So, the total probability is 0.0769 + 0.25 - 0.0192 = 0.3077.
Rounded to two decimal places, the probability that you will get a three or a diamond is 0.31.
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