48. The number of trucks passing by a gas station on a highway is to the number of passenger cars passing by the same highway as $3: 2$. It is known that on average, 1 out of 30 trucks and 2 out of 45 passenger cars pull up to the gas station for refueling. What is the probability that a vehicle arriving at the gas station will be refueled?
Solution. Consider the events:

$B_{1}$ - a truck has pulled up to the gas station;

$B_{2}$ - a car has pulled up to the gas station;
$A$ - the vehicle that has pulled up to the gas station will be refueled.

Given that the number of trucks is to the number of cars as $3: 2$, we find the probabilities of the hypotheses - events $B_{1}$ and $B_{2}: P\left(B_{1}\right)=0.6$, $P\left(B_{2}\right)=0.4$. The hypotheses $B_{1}$ and $B_{2}$ form a complete group of mutually exclusive events; the sum of the probabilities of these events is 1.

Event $A$ can only occur together with event $B_{1}$ or with event $B_{2}$. The conditional probability $P_{B_{1}}(A)=1 / 30$; the conditional probability $P_{B_{2}}(A)=2 / 45$.

Let's find the probability of event $A$, applying formula (16) for $n=2$:

$$
P(A)=P\left(B_{1}\right) \cdot P_{B_{1}}(A)+P\left(B_{2}\right) \cdot P_{B_{2}}(A)=0.6 \cdot \frac{1}{30}+0.4 \cdot \frac{2}{45} \approx 0.0378
$$