Question

Find the probability of atleast three successes in six trials of a binomial experiment in which the probability of success is 50%.

Answer 1

The binomial cumulative probability with p=0.5 for 3+ successes is as follows:

$P(3+)=\sum_{k=3}^6 {{6}\choose{k}}p^k(1-p)^{6-k}$

for p=0.5 (50% success rate) it becomes:

$P(3+)=\sum_{k=3}^6 {{6}\choose{k}}0.5^6=\frac{21}{32}=0.65625$

the probability is 0.65625, or about 66%