Question

The athletic director at Silvergrove High School counted the number of students on each winter sports team.
basketball 32
wrestling 10
gymnastics 4
ice hockey 16
swimming 10
What is the probability that a randomly selected winter athlete is on the gymnastics team?
Write your answer as a fraction or whole number.
P(gymnastics)=

Answer 1

To find the probability that a randomly selected winter athlete is on the gymnastics team, we first need to determine the total number of winter athletes.

We can do this by adding the number of students on each winter sports team:

- Basketball: 32
- Wrestling: 10
- Gymnastics: 4
- Ice Hockey: 16
- Swimming: 10

Now, we calculate the total:

\[
\text{Total students} = 32 + 10 + 4 + 16 + 10 = 72
\]

Next, we need to find the number of students on the gymnastics team, which is 4.

The probability \( P(\text{gymnastics}) \) is given by the formula:

\[
P(\text{gymnastics}) = \frac{\text{Number of students on gymnastics}}{\text{Total number of students}}
\]

Substituting in the values we found:

\[
P(\text{gymnastics}) = \frac{4}{72}
\]

To simplify this fraction, we divide both the numerator and the denominator by their greatest common divisor, which is 4:

\[
P(\text{gymnastics}) = \frac{4 \div 4}{72 \div 4} = \frac{1}{18}
\]

Thus, the probability that a randomly selected winter athlete is on the gymnastics team is:

\[
\boxed{\frac{1}{18}}
\]