SOLUTION: A box contains 7 black, 3 red, and 5 purple marbles. Consider the two-stage experiment of randomly selecting a marble from the box, replacing it, and then selecting a second marble

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Question 1041975: A box contains 7 black, 3 red, and 5 purple marbles. Consider the two-stage experiment of randomly selecting a marble from the box, replacing it, and then selecting a second marble. Determine the probabilities of the events in the following. List the sample space
a)Selecting 2 black marbles. Give answer as a simplified fraction.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Replacing the previously drawn marble makes the second selection an experiment independent of the first selection. The probability of both marbles being black is then %287%2F15%29%2A%287%2F15%29+=+49%2F225.
The sample space consists of all ordered pairs (x,y), where x and y get their values from the set { b%5Bi%5D, r%5Bj%5D, p%5Bk%5D }, where
i = 1,2,3,4,5,6,7,
j = 1,2,3, and
k = 1,2,3,4,5.
There are 15%5E2+=+7%5E2%2B3%5E2%2B5%5E2+%2B+2%2A%287%2A3%2B3%2A5%2B7%2A5%29+=+225 elements to this sample space.