Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 9, p = 0.1, P(Fewer tha

Question

Determine the indicated probability for a binomial experiment with the given number of trials n and the given success probability p. n = 9, p = 0.1, P(Fewer than 4)

Answer 1

It is a binomial random variable, so use the formulas for the binomial.

 

P(X=k) = n!/(k!(n-k)!) p^k(1-p)^(n-k)   n=9, p=0.1 and k=0, 1, .., 9

 

P(X<4) = P(X=0)+P(X=1)+P(X=2)+ P(X=3).

 

So use the first formula for k=0, 1, 2, and 3 to find the individual probabilities and then sum the up.