4. A die is rolled. Find the probability that: a) an even number of points will fall (event $A$); b) a number of points divisible by 3 will fall (event $B$); c) any number of points except 5 will fall (event $C$).
Solution. a) On the faces of a die, there are three even numbers (2, 4, and 6), i.e., the number of favorable outcomes $m=3$. The number of all possible outcomes is 6 (any number of points from 1 to 6 can fall). Therefore, $P(A)=3 / 6=1 / 2$.

b) Here, there are two numbers that are multiples of three: 3 and 6. Thus, $m=2$, and the number of all possible outcomes $n=6$, from which $P(B)=2 / 6=1 / 3$.

c) The favorable outcomes are the numbers $1, 2, 3, 4, 6$ - there are five of them $(m=5)$. The number of all possible outcomes $n=6$. Therefore, $P(C)=5 / 6$.