Two marbles are drawn at random and without replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events: A = two red marbles are drawn; B = two green marbles are drawn; C = two blue marbles are drawn; D =two marbles of the same color are drawn; Find the probabilities of the following events: (a) P(A), P(B), P(C), and P(D). (b) P(A | D)
A. On the 1st draw P(red) = 2/9 On the second draw P(red) = 1/8 Do you understand and can you find the overall probability of two red marbles?
I think I understand it. So basically, after that, you multiply the two draws correct?
I think I can find B and C. However, I don't get how to do D.
Drawing two reds, two greens or two blues are independent and mutually exclusive events. Therefore P(2 same color) = P(2 red) + P(2 green) + P(2 blue)
Ah, I see. Now I know what to do now and I've also got what to do for b) as well. Thanks! :)
You're welcome :) And yes for P(A), P(B) and P(C) you multiply the probabilities for each of the 2 draws to find the overall probability.
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