Question

A survey was taken by 120 people revealed that 45 people prefer to drive to work while 75 prefer to take the bus. One person was randomly chosen from this group. What is the probability that the chosen person prefers to take the bus? Write your answer as a ratio in simplest form.
1 point
45/120
5/8
20/24
13/30

Answer 1

To find the probability that a randomly chosen person prefers to take the bus, we need to use the formula for probability:

\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]

In this case, the number of favorable outcomes is the number of people who prefer to take the bus, which is 75. The total number of outcomes is the total number of people surveyed, which is 120.

So, the probability \( P \) that a randomly chosen person prefers to take the bus is:

\[
P = \frac{75}{120}
\]

Next, we simplify this fraction:

1. Find the greatest common divisor (GCD) of 75 and 120.
- The factors of 75 are 1, 3, 5, 15, 25, 75.
- The factors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120.
- The GCD is 15.

2. Divide both the numerator and denominator by the GCD (15):

\[
\frac{75 \div 15}{120 \div 15} = \frac{5}{8}
\]

Thus, the probability that the chosen person prefers to take the bus is:

\[
\frac{5}{8}
\]

The answer in simplest form is **5/8**.