Question 175661: Diana has a box containing 6 blue, 8 red, 5 purple, 9 green, and 2 clear marbles that are all the same size and shape. What is the probability of randomly choosing a clear marble on the first pick; replacing it, and then randomly choosing a purple marble on the second pick?
Found 4 solutions by checkley75, jim_thompson5910, gonzo, tom tom:
Answer by checkley75(3666)   (Show Source):
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website! Take note that there are 30 marbles (6 blue + 8 red + 5 purple + 9 green + 2 clear = 30 total)
P(picking clear marble on first pick) = # of clear marbles/# total = 2/30 = 1/15
Since the first marble was replaced, this means that
P(picking purple marble on second pick) = # of purple marbles/# total = 5/30 = 1/6
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Now the chances of the two events occurring are:
P(picking clear marble on first pick AND picking purple marble on second pick) = P(picking clear marble on first pick) * P(picking purple marble on second pick) = (1/15)(1/6)=1/90
So the probability is 1/90
Answer by gonzo(654) (Show Source):
You can put this solution on YOUR website! 6 blue
8 red
5 purple
9 green
2 clear
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30 total
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probability of getting a clear marble on the first pick is 2/30 because there are 2 clear marbles out of a total of 30 marbles in the box.
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probability of getting a purple marble on the second pick regardless of what was chosen on the first pick is 5/30 because there are 5 purple marbles out of a total of 30 marbles in the box once again since you put the marble you took on the first pick back in the box.
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the probability of getting a clear marble on the first pick, putting it in the box, and then getting a purple marble on the second pick is 2/30 * 5/30.
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if the probability of an event happening is x, and the probability of another event happening is y, then the probability of both events happening is x*y.
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by replacing the clear marble in the box, you made the two individual events independent of each other. if you did NOT replace the clear marble, then the probability of getting a purple marble on the second pick would have changed.
in that case it would have been 5/29 rather than 5/30.
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Answer by tom tom(1) (Show Source):
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