Question: Suppose the probability that a certain type of machine will work is 0.65. let X be the random variable that counts the number of machines that work in a group of 4 machines. Find the mean and standard deviation of X.
a. Find the probability that at least one machine will work.
b. Find P(X=2)  Edit

Answer: Let p be the probability of success i.e machine will work, and q be the failure i.e machine will not work. Then p=0.65 ; q=1-p=1-0.65=0.35 and n=4 This is a binomial distribution. In binomial experiment we know, P(x=i) = nCi p^i q^(n - i) a. P(x<1)=P(x=0) =4C0 * (0.65)^0 * (0.35)^4 =0.01500625 So, P(at least one machine will work)=1-0.01500625 =0.98499375 = 98.5% (Ans.) b. P(x=2)= 4C2*(0.65)^2*(0.35)^2 = 0.3105375 (Ans.)  Edit