A machine performs an operation (sizy- multiplication) correctly, with probability 0.9. The machine performs three successive multiplications. Assuming independence, find the probability of (a) Three...

A machine performs an operation (sizy- multiplication) correctly,

with probability 0.9. The machine performs three successive

multiplications. Assuming independence, find the probability

of

(a) Three correct multiplications

(b) Exactly one failure in the three multiplications

(c) No correct multiplications

(d) Exactly one success in the three multiplications

What is the sum of the probabilities in (a) through (d)? Why?