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

From a lot of 10 missiles, 4 are selected at random and fired. If the lot contains three defective missiles that will not fire, what is the probability that: all 4 will fire? at most 2 will not fire?

Solution

q2)probaility of defective missile=3/10

probability that all 4 will fire=7/10*6/9*5/8*4/7 =1/6 or .166

probability that at most donot fire=1-P(at least 2 fire) =1-3/10*2/9*1/8 =.9916

3)The probability of getting success after 1st success occurs is =pq^(x-1)

here x=4 p=1/2 q=1/2

probability =1/2 *(1/2)^4-1

              =1/16

q4) exactly 4 probability is

P(X=4)=P(X<=4)-P(X<=3) =.2851-.1512 =.1339

AT LEAST 4

P(X>=4)=1-P(X<=4) =1-.1512 =.8488