Question

the diagram shows the sports played by 80 students. if a student is picked at random, what is the probability that they play football?

Explanation:

Step1: Calculate the number of students who play football

Add up all the numbers in the football - related parts of the Venn diagram: \(4 + 14+31 + 5=54\)

Step2: Use the probability formula

The probability formula is \(P(A)=\frac{n(A)}{n(S)}\), where \(n(A)\) is the number of favorable outcomes and \(n(S)\) is the total number of outcomes. Here, \(n(A) = 54\) (number of students who play football) and \(n(S)=80\) (total number of students). So the probability \(P=\frac{54}{80}=\frac{27}{40}\)

Answer:

\(\frac{27}{40}\)