SOLUTION: Suppose a coin is tossed three times: a. What is the probability of getting exactly two heads? b. What is the probability of getting at least one tail?

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Question 867192: Suppose a coin is tossed three times:
a. What is the probability of getting exactly two heads?
b. What is the probability of getting at least one tail?
Found 2 solutions by ewatrrr, drvidmar:
Answer by ewatrrr(24785) About Me  (Show Source):
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Hi

P+%28x%29=+highlight_green%28nCx%29%28p%5Ex%29%28q%29%5E%28n-x%29+ 

p and q = .5,  n = 3

 

P( at least one tail) = 1 - P(none) = 1- (.5)^3 = .875

Answer by drvidmar(5) About Me  (Show Source):
You can put this solution on YOUR website!
a.
There are 8 possible results if you toss the coin three times, all equally likely: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT. In three of those results, you get exactly 2 heads: HHT, HTH, THH. Since there are three results with two heads out of eight possible results, the probability is three out of eight, or 3/8, or 37.5%.
b.
Following the same method as in (a), all of the possible results have at least one tail except HHH. Thus, the the probability of getting at least one tail is seven out of eight, or 7/8, or 87.5%.