Chapter 7.CRE, Problem 43CRE

QUALITY CONTROL Copykwik has four photocopy machines: $A$, $B$, $C$, and $D$. The probability that a given machine will break down on a particular day is

$P\left(A\right)=\frac{1}{50}$, $P\left(B\right)=\frac{1}{60}$, $P\left(C\right)=\frac{1}{75}$, $P\left(D\right)=\frac{1}{40}$

Assuming independence, what is the probability on a particular day that:

a. All four machines will break down?

b. None of the machines will break down?