Bernoulli Trials

xmathgurl101x · #1 $Old$ October 29th, 2009, 06:58 PM

Hey guys I'm new to this forum and I am having some difficulty with a certain problem concerning Bernoulli Trials.

Eight Bernoulli Trials are performed with probability p for success. Pr(no success) = Pr(2 successes). Calculate p and the Pr(1 success)(simplify to fraction in lowest term)

Any help of this problem would be great. Thanks!

theodds · #2 $Old$ October 29th, 2009, 08:41 PM

The sum of N identical Bernoulli RV's is a binomial(N, p) [call the sum X], p being the parameter for the Bernoulli. The first step is to find p, which you can get by solving $P(X = 2) = P(X = 0)$ for the parameter p, noting that for the general binomial random variable that $P(X = x) = \binom{n}{x} p^x (1-p)^{n - x}$ .