24. In a money and goods lottery, for every 1000 tickets, there are 5 monetary and 20 goods prizes. What is the probability of winning on one ticket?
S o l u t i o n. Consider the events:

$A_{1}$ - a material prize for one ticket;

$A_{2}$ - a monetary prize for one ticket;

$A$ - any prize for one ticket.

$A_{1}$ and $A_{2}$ are mutually exclusive events. Event $A$ consists in the occurrence of either event $A_{1}$ or event $A_{2}$ (it does not matter which); this means that event $A$ is the sum of events $A_{1}$ and $A_{2}: A=A_{1}+A_{2}$. We will find the probabilities of events $A_{1}$ and $A_{2}$, using formula (1): $P\left(A_{1}\right)=5 / 1000=0.005 ; P\left(A_{2}\right)=20 / 1000=0.02$.

The probability of event $A$ will be found using the theorem of the addition of probabilities of mutually exclusive events. According to formula (8), the required probability is

$$
P(A)=P\left(A_{1}+A_{2}\right)=0.005+0.020=0.025
$$