Question

The 10th grade class at Central high school was surveyed about whether they liked running or swimming. Of those surveyed, 58% said they liked to swim and 36% said they liked to run. If 18% said they liked both swimming and running, what percent of those surveyed liked neither?

Answer 1

Answer:

24% of those surveyed liked neither

Step-by-step explanation:

Set concepts:

We use set concepts to solve this question.

I am going to say that:

P(A) is the percentage of people that liked to swim.

P(B) is the the percentage of people that liked to run.

The percentage of people that liked at least one of these activities is:

$P(A \cup B) = P(A) + P(B) - P(A \cap B)$

In which $P(A \cap B)$ is the probability that a person liked both these activities.

The percentage of people that liked neither is:

$P = 1 - P(A \cup B)$

Of those surveyed, 58% said they liked to swim and 36% said they liked to run.

This means that $P(A) = 0.58, P(B) = 0.36$

18% said they liked both swimming and running

This means that $P(A \cap B) = 0.18$

What percent of those surveyed liked neither?

At least one:

$P(A \cup B) = 0.58 + 0.36 - 0.18 = 0.76$

Neither:

$P = 1 - P(A \cup B) = 1 - 0.76 = 0.24$

24% of those surveyed liked neither