SOLUTION: In a box there are five doughnuts, and Alice takes two of them at random. Out of the five doughnuts, three are cream-filled, and two are not. What is the probability that Alice obt

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Question 1152128: In a box there are five doughnuts, and Alice takes two of them at random. Out of the five doughnuts, three are cream-filled, and two are not. What is the probability that Alice obtains exactly one creamed-filled doughnut in the two she takes out of the box?
Answer by greenestamps(13200) About Me  (Show Source):
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Number of possible choices of 2 doughnuts out of the 5: 5 choose 2.

Number of possible choices of 1 out of the 3 cream-filled doughnuts AND 1 of the 2 others: (3 choose 1) times (2 choose 1).

P(1 cream-filled) = %28C%283%2C1%29%2AC%282%2C1%29%29%2FC%285%2C2%29+=+%283%2A2%29%2F10+=+3%2F5

Alternate solution method:

P(one cream-filled and one not)
= P((cream-filled first AND not cream-filled second) OR (not cream-filled first AND cream-filled second))
= %283%2F5%29%282%2F4%29%2B%282%2F5%29%283%2F4%29+=+6%2F20%2B6%2F20+=+12%2F20+=+3%2F5