SOLUTION: In a bag are 4 yellow and 8 blue marbles. 3 are selected at random without replacement. What is the probability that all 3 are yellow or all 3 are blue?

Question 617401: In a bag are 4 yellow and 8 blue marbles. 3 are selected at random without replacement. What is the probability that all 3 are yellow or all 3 are blue?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
P(3 yellow) = (4/12)*(3/11)*(2/10) = 24/1320 = 1/55

P(3 blue) = (8/12)*(7/11)*(6/10) = 336/1320 = 14/55

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P(3 Yellow OR 3 Blue) = P(3 yellow) + P(3 blue)

P(3 Yellow OR 3 Blue) = 1/55 + 14/55

P(3 Yellow OR 3 Blue) = 15/55

P(3 Yellow OR 3 Blue) = 3/11

Note: we can simply add the probabilities because the two events are mutually exclusive.

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