SOLUTION: A coin is tossed 6 times. Find the probabilities of getting the following: a.) Exactly 3 heads

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Question 206795: A coin is tossed 6 times. Find the probabilities of getting the following:
a.) Exactly 3 heads

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
A coin is tossed 6 times. Find the probabilities of getting the following:
a.) Exactly 3 heads

Here is the binomial rule:

If p is the probability of getting 1 success in 1 trial,
and n is the number of trials, and q=1-p, then the 
probability of getting exactly r successes out of the n 
trials is

%28nCr%29%28p%5Er%29%28q%5E%28n-r%29%29

Here a success will be a head on a coin, and a trial
will be a toss. Here p=1%2F2 is the probability 
of getting 1 head in 1 trial. There are 6
trials (tosses), so n=6. Then the probability of 
getting exactly 3 heads out of the 6 trials 
is gotten by substituting in that expression, with 
q=1-p=1=1%2F2=1%2F2.

%286C3%29%281%2F2%29%5E3%281%2F2%29%5E%286-3%29
%28%286%2A5%2A4%29%2F%283%2A2%2A1%29%29%281%2F2%29%5E%283%29%281%2F2%29%5E%283%29
%28120%2F6%29%281%2F2%29%5E3%281%2F2%29%5E3
%2820%29%281%2F8%29%281%2F8%29
%2820%29%281%2F64%29
5%2F16%29

Edwin