A box contains 6 identically sized, solid-colored balls. One ball is green, 2 are yellow, and 3 are red. A ball is drawn at random and returned to the box, then a second ball is drawn at random. What is the probability that the first ball is red and the second ball is green?
Question
A box contains 6 identically sized, solid-colored balls. One ball is green, 2 are yellow, and 3 are red. A ball is drawn at random and returned to the box, then a second ball is drawn at random. What is the probability that the first ball is red and the second ball is green?
Solution
To solve this problem, we need to calculate the probability of each event separately and then multiply them together because these are independent events.
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Calculate the probability of drawing a red ball first. There are 3 red balls out of a total of 6 balls. So, the probability is 3/6 = 0.5.
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Calculate the probability of drawing a green ball second. Since the first ball was returned to the box, there are still 6 balls in the box. There is 1 green ball, so the probability is 1/6.
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Multiply the two probabilities together to get the overall probability. So, 0.5 * 1/6 = 0.0833 or 8.33%.
So, the probability that the first ball drawn is red and the second ball drawn is green is 8.33%.
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