Question

1. in a music school of 124 students, 82 students play the piano, 71 students play the guitar and 10 students play neither. 7c what is the probability that a student chosen at random plays the piano or the guitar? (venn diagram with piano circle: 43, overlap: 39, guitar circle: 32, outside both: 10)

Explanation:

Step1: Find number of students who play piano or guitar

From the Venn diagram, the number of students who play piano or guitar is \(43 + 39 + 32\).
\(43+39 + 32=114\)

Step2: Calculate the probability

The total number of students is \(124\). The probability is the number of students who play piano or guitar divided by total number of students.
Probability \(=\frac{114}{124}\)
Simplify the fraction: \(\frac{114\div2}{124\div2}=\frac{57}{62}\)

Answer:

\(\frac{57}{62}\)