SOLUTION: A fair coin tossed 5 times. Find the probability that exactly 3 heads appear.

Question 161466: A fair coin tossed 5 times. Find the probability that exactly 3 heads appear.
Answer by ilana(307) (Show Source): You can put this solution on YOUR website!
First, look at a simple situation where this occurs (called a success): HHHTT, so first 3 flips are heads, last 2 are tails. The probability that this occurs is .5*.5*.5*.5*.5, or (.5)^5, or 0.03125. But another success is HHTTH, which has the same probability, 0.03125. So the probability that one of those occurs is 0.03125+0.03125, or 0.0625. Actually, a success happens in many more cases. The number of these successes is 5!/(3!*2!), or 10, since that is the number of different ways you can choose 3 of those flips to be heads. So the probablity that exactly 3 are heads is 10*0.03125, or 0.3125, or about 31%.
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