SOLUTION: A bag contains 3 black and 2 white balls. Two balls are taken from the bag at random, without replacement. By drawing a tree diagram, or otherwise, calculate the probability that

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Question 1196513: A bag contains 3 black and 2 white balls. Two balls are taken from the bag at random, without replacement. By drawing a tree diagram, or otherwise, calculate the probability that
(a) both balls are black,
(b) at least one ball is white,
(c) the two balls are the same colour.
Found 2 solutions by ikleyn, ewatrrr:
Answer by ikleyn(52795) About Me  (Show Source):
You can put this solution on YOUR website!
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Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!

Hi  
Previously Solved
5 Balls: 3B,2W
Two balls are taken from the bag at random, without replacement.
(a) P(both balls are black) = 3C2/5C2 = 3/10
(b) P(at least one ball is white) = 1 - 3/10 = 7/10:
(c) P(the two balls are the same color) = P(both Black OR both White)
P =  3/10 +  2C2/5C2 = 3/10 + 1/10 = 4/10 
Wish You the Best in your Studies.