Problem 1. The probability that a shooter, upon firing a shot, will score 10 points is 0.4; 9 points - 0.3; and finally, 8 or fewer points - 0.3. Find the probability that the shooter will score no less than 9 points in one shot.
Solution. Let's denote the events and write down the corresponding probabilities:

$A$ - hitting $10, p(A)=0.4$;

$B$ - hitting $9, p(B)=0.3$;

$C$ - hitting 8 or less, $p(C)=0.3$.

$A+B-$ hitting either 10 or $9, p(A+B)=$ ?

Since events $A, B, C$ are mutually exclusive, by formula (6) we have:

$$
p(A+B)=p(A)+p(B)=0.4+0.3=0.7
$$