Garrett has a bag of marbles with 2 blue marbles, 2 white marbles, and 2 red marbles. Find the following probabilities of Garrett drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn. a) A Blue, then a red = b) A red, then a white = c) A Blue, then a Blue, then a Blue =
Question
Garrett has a bag of marbles with 2 blue marbles, 2 white marbles, and 2 red marbles.
Find the following probabilities of Garrett drawing the given marbles from the bag if the first marble(s) is(are) returned to the bag after they are drawn.
a) A Blue, then a red =
b) A red, then a white =
c) A Blue, then a Blue, then a Blue =
Solution
a) The probability of drawing a blue marble is 2 out of 6 (or 1/3), and the probability of drawing a red marble is also 2 out of 6 (or 1/3). Since the marbles are returned to the bag after each draw, these events are independent, so we multiply the probabilities together to get the overall probability. So, the probability of drawing a blue marble and then a red marble is (1/3) * (1/3) = 1/9.
b) Similarly, the probability of drawing a red marble is 2 out of 6 (or 1/3), and the probability of drawing a white marble is also 2 out of 6 (or 1/3). So, the probability of drawing a red marble and then a white marble is (1/3) * (1/3) = 1/9.
c) The probability of drawing a blue marble is 2 out of 6 (or 1/3). Since the marbles are returned to the bag after each draw, the events are independent, so we multiply the probabilities together for each draw. So, the probability of drawing a blue marble three times in a row is (1/3) * (1/3) * (1/3) = 1/27.
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