The problem asks us to find the probability that a randomly selected winter athlete at Silvergrove High School is on the gymnastics team. We are given the number of students on each winter sports team: basketball (32), wrestling (10), gymnastics (4), ice hockey (16), and swimming (10). We need to express the probability as a fraction or whole number.

1. Problem Description

The problem asks us to find the probability that a randomly selected winter athlete at Silvergrove High School is on the gymnastics team. We are given the number of students on each winter sports team: basketball (32), wrestling (10), gymnastics (4), ice hockey (16), and swimming (10). We need to express the probability as a fraction or whole number.

2. Solution Steps

First, we need to find the total number of winter athletes. We do this by summing the number of students in each sport:

$Total = Basketball + Wrestling + Gymnastics + Ice\ Hockey + Swimming$

$Total = 32 + 10 + 4 + 16 + 10 = 72$

Next, we need to find the probability that a randomly selected athlete is on the gymnastics team. The probability is given by the formula:

$Probability = \frac{Number\ of\ Gymnastics\ Students}{Total\ Number\ of\ Students}$

$P(gymnastics) = \frac{4}{72}$

Now, we simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is

4. $P(gymnastics) = \frac{4 \div 4}{72 \div 4} = \frac{1}{18}$

3. Final Answer

1/18