find the probability of at least 3 successes in 6 trials of a binomial experiment in which the probability of success is 50%

Answer 1

The probability of at least 3 successes means he could have exactly 3, 4, 5, or 6 successes.Let p = probability of success and q = probability of failure (.5 for both in this case).

The formula for exactly x successes in N trials is _NC_xp^xq^(N-x)

So P(At least 3 successes) = ₆C₃p³q^(6-3) + ₆C₄p⁴q^(6-4) + ₆C₅p⁵q^(6-5) + ₆C₆p⁶q^(6-6)

P(at least 3) = .3125 + .2344 + .0938 + .0156 = .6563