The binomial cumulative probability with p=0.5 for 3+ successes is as follows:
[tex]P(3+)=\sum_{k=3}^6 {{6}\choose{k}}p^k(1-p)^{6-k}[/tex]
for p=0.5 (50% success rate) it becomes:
[tex]P(3+)=\sum_{k=3}^6 {{6}\choose{k}}0.5^6=\frac{21}{32}=0.65625[/tex]
the probability is 0.65625, or about 66%
