86. The probability of at least one hit by a shooter on a target in three shots is 0.875. Find the probability of a hit in one shot.
Solution. The probability of hitting the target at least once in three shots (event $A$) is

$$
P(A)=1-q^{3} \text {, }
$$

where $q$ is the probability of a miss.

According to the condition, $P(A)=0.875$. Therefore,

$$
0.875=1-q^{3}, \text { or } q^{3}=1-0.875=0.125 \text {. }
$$

Hence, $q=\sqrt[3]{0.125}=0.5$.

The required probability

$$
p=1-q=1-0.5=0.5
$$