Task 1. Two shooters fired one shot each at a target. The probability of hitting the target for the first shooter is 0.7; for the second shooter, it is 0.8. Find the probability that at least one shooter will hit the target.
Solution. Let's denote the events:

$A_{1}$ - the first shooter hits the target;

$A_{2}$ - the second shooter hits the target;

Then $A_{1}+A_{2}$ - at least one shooter hits the target. Events $A_{1}$ and $A_{2}$ are compatible and independent, so by formula (15) we have:

$$
p\left(A_{\mathrm{I}}+A_{2}\right)=p\left(A_{1}\right)+p\left(A_{2}\right)-p\left(A_{1}\right) p\left(A_{2}\right)=0.7+0.8-0.56=0.94
$$

Problem 2. In a television studio, 2 cameras are installed, for each of which the probability that it is on at a given moment is $p=0.6$. Find the probability that at least one camera is on at a given moment.

Solution. Consider the events:

$A_{1}$ - the first camera is on at a given moment;

$A_{2}$ - the second camera is on at a given moment;

$A_{1}+A_{2}$ - at least one camera is on at a given moment.

Events $A_{1}, A_{2}$ - are compatible and independent, so by formula (15) we have:

$$
p\left(A_{\mathrm{I}}+A_{2}\right)=p\left(A_{\mathrm{I}}\right)+p\left(A_{2}\right)-p\left(A_{1}\right) p\left(A_{2}\right)=0.6+0.6-0.36=0.84
$$