Question

If X is a binomial random variable with n and p as indicated, compute the probabilities for each of the following cases:

P (X<3), n=8, p=.7

Answer 1

Solution:

We are given

n = 8

p = 0.7

q = 1 – p = 1 – 0.7 = 0.3

We have to find P(X<3)

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

P(X=x) = nCx*p^x*q^(n – x)

P(X=0) = 8C0*0.7^0*0.3^(7 – 0) = 0.00006561

P(X=1) = 8C1*0.7^1*0.3^(7 – 1) = 0.00122472

P(X=2) = 8C2*0.7^2*0.3^(7 – 2) = 0.01000188

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

P(X<3) = 0.00006561 + 0.00122472 + 0.01000188

P(X<3) = 0.01129221

Required probability = 0.01129221