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=(21)/(32)=0.65625`

the probability is 0.65625, or about 66%