Example 23. The probability that an event will occur at least once in three independent trials is 0.973. Find the probability of the event occurring in one trial (it is assumed that the probability of the event occurring is the same in all trials).


Solution. Since the events under consideration are independent in aggregate, formula (1.8.17) is applicable, i.e.

$$
P(A)=1-q^{n}
$$

By the condition

$$
P(A)=0.973, n=3
$$

Therefore,

$$
0.973=1-q^{3}
$$

or

$$
\begin{aligned}
& q^{3}=1-0.973=0.027 \\
& q=\sqrt[3]{0.027}=0.3
\end{aligned}
$$

The required probability

$$
p=1-q=1-0.3=0.7
$$