Question

In a music class of 20 students, there are 12 who play the Guitar (G), 7 who play the Piano (P) and 4 who do not play any of these instruments.1)Represent this situation using a Venn diagram2)What is the probability no randomly selected student plays guitar and piano3)What is the probability that no randomly selected student plays either of these two instruments?4) How likely is it that no randomly selected student plays the piano

Answer 1

GIVEN:

Total number of students: 20

Number that plays the Guitar: 12

Number that plays the Piano: 7

Number that does not play any of the instruments: 4

Note that included in the number that plays either the guitar and the piano is the number that plays both instruments. Let's call this number x.

Number that play both instruments: To calculate this number, we have to get the number that plays each instrument alone and find the sum equated to the total number of students.

Number that plays the Guitar only: 12 - x

Number that plays the Piano only: 7 - x

Therefore, the total number of students will be:

`\begin{gathered} 12-x+7-x+x+4=20 \\ 23-x=20 \\ \therefore \\ x=23-20 \\ x=3 \end{gathered}`

Hence, there are 3 students that play both instruments.

Therefore, 9 students play the guitar only and 4 students play the piano only.

VENN DIAGRAM:

QUESTION 2:

The formula to calculate the probability of an event E is given to be:

`P(E)=(n(E))/(n(U))`

where

`\begin{gathered} P(E)=\text{ Probability of event E happening} \\ n(E)=\text{ Number of times event E happened} \\ n(U)=\text{ Number of times all possible events occured} \end{gathered}`

The number of students that play the guitar and piano is 3. This means that the number that does not play the guitar and piano is

`\Rightarrow20-3=17\text{ students}`

Therefore, the probability is given to be:

`P=(17)/(20)`

QUESTION 3:

This question requires us to find the probability of students that do not play any of the two instruments. This number is 4.

Therefore, the probability is given to be:

`P=(4)/(20)=(1)/(5)`

QUESTION 4:

The number of students that play the piano is 7. Hence, the number that doesn't play the piano will be:

`\Rightarrow20-7=13`

Therefore, the probability is:

`P=(13)/(20)`