A jar contains seven blue marbles and five red marbles. Suppose you choose a marble at random, and do not replace it. Then you choose a second marble. Find the probability of the following event.
Both of the selected marbles are red.
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Part 1
The probability that both of the selected marbles are red is
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The probability that both of the selected marbles are red can be calculated as follows:
First, the probability of choosing a red marble on the first draw is 5/12 (since there are 5 red marbles out of 12 total marbles).
After the first red marble is chosen and not replaced, there are now only 11 marbles left in the jar, with 4 red marbles remaining. So, the probability of choosing a second red marble is 4/11.
Therefore, the overall probability of both marbles being red is:
(5/12) * (4/11) = 20/132 = 5/33
So, the probability of both selected marbles being red is 5/33.