Back 20:06Finish LaterSubmitA basket contains 10 solid-colored balls—2 blue, 3 red, and 5 green. Each ball has a single number printed on it. The blue balls are numbered 1 and 2 (each number is used once), the red balls are numbered 1-3 (each number is used once), and the green balls are numbered 1-5 (each number is used once). A ball will be drawn at random from the basket. What is the probability that the ball that is drawn will be red or have a 3 printed on it?
Question
Back 20:06Finish LaterSubmitA basket contains 10 solid-colored balls—2 blue, 3 red, and 5 green. Each ball has a single number printed on it. The blue balls are numbered 1 and 2 (each number is used once), the red balls are numbered 1-3 (each number is used once), and the green balls are numbered 1-5 (each number is used once). A ball will be drawn at random from the basket. What is the probability that the ball that is drawn will be red or have a 3 printed on it?
Solution
To solve this problem, we need to calculate the probability of drawing a red ball and the probability of drawing a ball with a 3 on it, and then add those probabilities together. However, we must be careful not to double count the red ball with a 3 on it.
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Calculate the probability of drawing a red ball: There are 3 red balls out of a total of 10 balls, so the probability of drawing a red ball is 3/10.
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Calculate the probability of drawing a ball with a 3 on it: There are 3 balls with a 3 on them (one red, one blue, and one green) out of a total of 10 balls, so the probability of drawing a ball with a 3 on it is 3/10.
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Add the probabilities together: The sum of the probabilities is 3/10 + 3/10 = 6/10.
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Adjust for double counting: We have counted the red ball with a 3 on it twice, so we need to subtract its probability from our total. The probability of drawing the red ball with a 3 on it is 1/10, so our final probability is 6/10 - 1/10 = 5/10 = 0.5.
So, the probability that the ball that is drawn will be red or have a 3 printed on it is 0.5.
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