Question 942430
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(X=r) = C(n,r)*(p^r)*(q^(n-r))}}}
where C(n,r) is r combinations out of n objects = {{{n!/((n-r)!r!)}}}
and q=(1-p)
  
Substituting values n=10, p=0.5, r=5 or 6, we get
{{{P(X=5) = C(10,5)*(0.5^5)*((1-0.5)^(10-5))=0.246}}}
{{{P(X=6) = C(10,6)*(0.5^6)*((1-0.5)^(10-6))=0.205}}}
  
Probability of 5 or 6 heads is the sum of P(X=5) and P(X=6) 
{{{P(X=5 or X=6)=0.246+0.205=0.451}}}