Suppose that three persons (A, B and C) throw at a target. And A throws 10 times with the probability 0.3 to hit the target; and B throws 15 times with the probability 0.2; and C throws 20 times with the probability 0.1. Now Determine the probability that the target will be hit at least 12 times.
My solution is as follows:
For each throw, the probability of hitting the target is
Pr(H=1) = Pr(A)Pr(A Hit) + Pr(B)Pr(B Hit) + Pr(C)Pr(C Hit)
Pr(H=1) = (10/45)*0.3 + (15/45)*0.2 + (20/45)*0.1 = 8/45
So, the throw distribution can be seemed as binomial distribution
H ~ Bin(45, 8/45)
then can get the answer.
Am I right to consider the target hit variable as a binomial distribution?
And please give me a help to get the correct answer, any hints will be appreciated. Thanks.