Question

the athletic director at silvergrove high school counted the number of athletes 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.

Explanation:

Step1: Calculate total number of athletes

First, we sum up the number of athletes in each sport. The numbers are 32 (basketball), 10 (wrestling), 4 (gymnastics), 16 (ice hockey), and 10 (swimming). So the total is \(32 + 10 + 4 + 16 + 10\).
\(32+10 = 42\), \(42 + 4 = 46\), \(46+16 = 62\), \(62 + 10 = 72\). So total athletes \(n = 72\).

Step2: Determine number of gymnastics athletes

The number of athletes in gymnastics \(m = 4\).

Step3: Calculate probability

Probability \(P\) is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, favorable outcomes are gymnastics athletes, so \(P=\frac{4}{72}\). Simplifying this fraction by dividing numerator and denominator by 4, we get \(\frac{4\div4}{72\div4}=\frac{1}{18}\).

Answer:

\(\frac{1}{18}\)