Question

A researcher surveyed 80 adults and found that 22 regularly run for exercise and 18 regularly swim for exercise.
The probability that a randomly chosen adult both runs and swims is 1/5.
What is the probability that a randomly chosen adult runs or swims?

Answer 1

Whenever the questions asks for the probability and has "or" you have to add the two probabilities. In the same way, "and" implies multiplication. Therefore, the probability that someone swims is:
$\frac{18}{80} = \frac{9}{40}$

Probability that someone runs:
$\frac{22}{80} = \frac{11}{40}$

Thus, if you add them:
$\frac{9}{40} + \frac{11}{40} = \frac{20}{40} = \frac{1}{2}$

So, the probability that someone swims or runs is 1/2 or 50%.