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)

Question

Two marbles are drawn at random and without replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define 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)

kropot72 · Answer

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?

anonymous · Answer

I think I understand it. So basically, after that, you multiply the two draws correct?

anonymous · Answer

I think I can find  B and C. However, I don't get how to do D.

kropot72 · Answer

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)

anonymous · Answer

Ah, I see. Now I know what to do now and I've also got what to do for b) as well. Thanks! :)

kropot72 · Answer

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.