Question

There are 108 flights from an airport, 20 of which are longer than 3 hours.

The flight from this airport will be randomly chosen.

What is the probability it is longer than 3 hours?

Enter your answer as a fraction in simplest form in the box.

Answer 1

To find the probability that a randomly chosen flight is longer than 3 hours, we can use the formula for probability:

\[
P(\text{Longer than 3 hours}) = \frac{\text{Number of flights longer than 3 hours}}{\text{Total number of flights}}
\]

From the problem, we know:

- Number of flights longer than 3 hours = 20
- Total number of flights = 108

Now we can substitute these values into the formula:

\[
P(\text{Longer than 3 hours}) = \frac{20}{108}
\]

Next, we simplify the fraction \(\frac{20}{108}\). We can find the greatest common divisor (GCD) of 20 and 108:

- Factor 20: \(20 = 2^2 \times 5\)
- Factor 108: \(108 = 2^2 \times 3^3\)

The GCD is \(2^2 = 4\).

Now we divide both the numerator and denominator by their GCD:

\[
\frac{20 \div 4}{108 \div 4} = \frac{5}{27}
\]

Thus, the probability that a randomly chosen flight is longer than 3 hours is:

\[
\boxed{\frac{5}{27}}
\]