74. Find the probability $P(\bar{A} \bar{B})$ given the following probabilities:

$$
P(A)=a, P(B)=b . \quad P(A+B)=c
$$
Solution. Using the identity $P(\bar{B})=P(A \bar{B})+P(\bar{A} \bar{B})$, we find $P(\bar{A} \bar{B}):$

$$
P(\bar{A} \bar{B})=P(\bar{B})-P(A \bar{B})=(1-b)-P(A \bar{B})
$$

Substituting into the last equality $P(A \bar{B})=c-b$ (see problem 73), we get

$$
P(\bar{A} \bar{B})=1-b-(c-b)=1-c
$$