SOLUTION: A fair coin is flipped 10 times. Find the probability of the occurrence of 5 or 6 heads.

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Question 942430: A fair coin is flipped 10 times. Find the probability of the occurrence of 5 or 6 heads.
Answer by mathmate(429) About Me  (Show Source):
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Given:
A fair coin
Flipped 10 times

This means that
1. probability of heads (success) is constant at p=0.5
2. "flipping 10 times" imply random and independent outcomes over the experiment
3. The number of trials (flip) is known.
4. Each trial is a Bernoulli experiment (one of two possible outcomes).
Under these conditions, the binomial distribution applies.

The probability of r successes in n trials is given by:
P%28X=r%29+=+C%28n%2Cr%29%2A%28p%5Er%29%2A%28q%5E%28n-r%29%29
where C(n,r) is r combinations out of n objects = n%21%2F%28%28n-r%29%21r%21%29
and q=(1-p)

Substituting values n=10, p=0.5, r=5 or 6, we get
P%28X=5%29+=+C%2810%2C5%29%2A%280.5%5E5%29%2A%28%281-0.5%29%5E%2810-5%29%29=0.246
P%28X=6%29+=+C%2810%2C6%29%2A%280.5%5E6%29%2A%28%281-0.5%29%5E%2810-6%29%29=0.205

Probability of 5 or 6 heads is the sum of P(X=5) and P(X=6)
P%28X=5+or+X=6%29=0.246%2B0.205=0.451