63. A large batch of car tires contains $1.5\%$ defects. What should be the volume of a random sample so that the probability of finding at least one defective car tire in it would be more than $0.92?$
S o l u t i o n. Let the volume of the random sample be denoted by $n$. The experiment consists of checking car tires. Event $A$, which may or may not occur in each trial, is that the checked car tire turns out to be defective. The probability $p=0.015$; the probability $q=0.985$. Consider the events:

C - the sample of checked car tires contains at least one defective tire;

$\bar{C}$ - the sample of checked car tires contains no defective tires.

Using formulas (11) and (18), we get:

$$
P(C)=1-P(\bar{C})=1-P_{n}(0)=1-q^{n}=1-(0.985)^{n}
$$

By the condition $P(C)>0.92$. Thus, to find $n$, we need to solve the inequality:

$$
1-(0.985)^{n}>0.92
$$

Sequentially, we find

$$
(0.985)^{n}<0.08
$$

$$
n>\frac{\ln 0.08}{\ln 0.985} \approx 167.1608
$$

Thus, the random sample should contain no fewer than 168 car tires.