4 From a lot of 10 missiles 4 are selected at random and fir

(4) From a lot of 10 missiles, 4 are selected at random and fired. If a lot contains 3 defective missiles that will not fire, what is the probability that (a) all 4 will fire ? (b) at most two will fire ?

Solution

X no of missiles that fire follows a binomial distribution with p = 1-0.3 = 0.7

As 4 are selected, n =4

a) all 4 will fire = P(X=4) = 0.2401

b) at most 2 will not fire = atleast 2 will fire

P(X>=2) = 0.9163.