Binomial distribution for JEE

Formula

If \(X\sim B(n,p)\), then \(P(X=r)=\binom{n}{r}p^r q^{n-r}\), \(r=0,1,2,\dots,n\), \(q=1-p\); \(E(X)=np\), \(\operatorname{Var}(X)=npq\)

Variables: \(n\): number of independent trials, \(p\): success probability, \(q=1-p\).

Conditions: Independent identical Bernoulli trials.

Number of successes in repeated trials.