Example 18. In a workshop, two motors are working independently of each other. The probability that the first motor will not require the master's attention during an hour is 0.85, and for the second motor, this probability is 0.8. Find the probability that during the hour neither of the motors will require the master's attention.
Solution. We introduce notations for events: $A$ - "the first motor will not require the master's attention during an hour", $B$ - "the second motor will not require attention during an hour". Let's find the probability of the event $A B$. Since $A$ and $B$ are independent events, then $\cdot$

$$
P(A B)=P(A) P(B)=0.85 \cdot 0.8=0.68
$$