An engineering system consisting of components is said to be a -out-of-system (k ≤ n) if the system functions if and only if at least k of the n components function. Suppose that all components function independently of one another.

a. If the ith component functions with probability p_i, i = 1, 2, 3, 4, compute the probability that a 2-out-of-4 system functions.

b. Repeat part (a) for a 3-out-of-5 system.

c. Repeat for a -out-of- system when all the P_i equal (that is, P_i = p, i = 1, 2, ..., n).