The problem describes a bus transporting students for a multisport competition. Initially, there are 10 ping-pong players, 12 runners, and 18 gymnasts. After a stop, they all get back on the bus, and a group of swimmers get on as well. The probability that the first person to get off the bus is a swimmer is $1/5$. The goal is to determine the total number of people on the bus after the swimmers get on.

1. Problem Description

The problem describes a bus transporting students for a multisport competition. Initially, there are 10 ping-pong players, 12 runners, and 18 gymnasts. After a stop, they all get back on the bus, and a group of swimmers get on as well. The probability that the first person to get off the bus is a swimmer is $1/5$. The goal is to determine the total number of people on the bus after the swimmers get on.

2. Solution Steps

First, we calculate the total number of students on the bus before the swimmers get on.

Total students = ping-pong players + runners + gymnasts

Total students = $10 + 12 + 18 = 40$

Let $x$ be the number of swimmers who get on the bus. After the swimmers get on, the total number of people on the bus is $40 + x$.

The probability that the first person to get off the bus is a swimmer is given as $1/5$.

This can be written as:

$P(\text{first person is a swimmer}) = \frac{\text{Number of swimmers}}{\text{Total number of people on the bus}}$

We are given that $P(\text{first person is a swimmer}) = \frac{1}{5}$.

So,

$\frac{x}{40 + x} = \frac{1}{5}$

Now we solve for $x$:

$5x = 40 + x$

$4x = 40$

$x = 10$

Therefore, there are 10 swimmers on the bus. The total number of people on the bus is $40 + x = 40 + 10 = 50$.

3. Final Answer

The total number of people on the bus is 50.