Question

to get to know her students better, ms. alexander surveyed her math students to determine what hobbies and school subjects they prefer.
athletics the arts
math 1 2
literature 3 4
what is the probability that a randomly selected student prefers math or prefers athletics?
simplify any fractions.

Explanation:

Step1: Calculate the total number of students

Total number of students \(=1 + 2+3 + 4=10\)

Step2: Calculate the number of students who prefer math or athletics

Number of students who prefer math \(=1 + 2 = 3\)
Number of students who prefer athletics \(=1+3 = 4\)
Number of students who prefer both math and athletics \(=1\)
Using the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\)
\(n(\text{math}\cup\text{athletics})=3 + 4-1=6\)

Step3: Calculate the probability

Probability \(P=\frac{n(\text{math}\cup\text{athletics})}{\text{Total number of students}}=\frac{6}{10}=\frac{3}{5}\)

Answer:

\(\frac{3}{5}\)