Question

In a group of 31 pupils, 4 play the flute only. 14 play the piano only. 7 play neither instrument. A student is selected at random. What is the probability the student plays both instruments?

Answer 1

Note that:

• Total pupils: 31
• 4 pupils = flute only
• 14 pupils = piano only
• 7 pupils = neither
• This means that {31 - (4 + 14 + 7)} pupils play both instruments.

First, let's find out the number of pupils who play both instruments.

• => {31 - (4 + 14 + 7)} pupils
• => {31 - (25)} pupils
• => {31 - 25} pupils
• => 6 pupils

Probability form: Student who plays both instruments/Total students

• => 6/31

The probability that this student plays both instruments is 6/31.

Answer 2

probability the student plays both instruments is [
`(6)/(31)` ]

Step-by-step explanation:

students who play both instruments = total students - flute players - piano players - students who play neither instruments

students who play both instruments

→ 31 - 4 - 14 - 7

→ 6 students play both instruments.

probability:

→
`\boxed{(students- who -play- both- instruments)/(total -students) }`

→
`\boxed{(6)/(31) }`