Question 1150020: A bag contains 7 red apples and 6 yellow apples. A sample of 3 apples is drawn. Find the probability that the sample contains more red than yellow apples.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the number of samples of 3 apples is 13C3, which is 286
more red than yellow occurs with 3 red and 0 yellow and 2 red and 1 yellow
those occur 7C3 of the time for the first (which is 35) and 7C2*6C1, which is 21*6 or 126 times
those add to 161
the probability is 161/286=0.5629
Another way, longer is probability all 3 apples are red is 7/13*6/12*5/11=0.1224
and 1 is yellow, and there are 3 ways to do that, all with the same denominator of 13*12*11
the numerator has the 3 numbers ordered 3 different ways, so it is 3*7*6*6=756
756/1716=0.4406
those add to 0.5630, the difference being rounding error. The first is more exact.
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