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5 votes
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?

User RunningAdithya
by
3.1k points

2 Answers

22 votes
22 votes

Solution:

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.

User Fission
by
2.2k points
19 votes
19 votes

Answer:

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) }

User Gletscher
by
2.7k points