Question

The students of a high school are 51% males. Of the students at this high school 45% of males and 40% of females said they regularly attend concerts.

Answer 1

(b) Probability that a student is male and attends concert = 22.95%

(c) Probability that a student is female and does not attend concert = 29.4%

(d) Probability that a student attends concerts = 42.55%

Explanation:

P.S - The exact question is -

Given - The population of a high school is 51% male. 45% of the males and 40% of the females attend concerts.

To find - (a) Make a tree diagram based on the information above.

(b) Find the probability that a student is male and attends

concerts.

(c) Find the probability that a student is female and does not

attend concerts.

(d) Find the probability that a student attends concerts.

Proof -

Let the total population of the high school = 100 x

Given that,

The students of a high school are 51% males

⇒Total males in the high school = 51% × 100 x

=
`(51)/(100)` × 100 x = 51 x

⇒Total males in the high school = 51 x

⇒Total females in the high school = 100 x - 51 x = 49 x

Now,

Given that,

Of the students at this high school 45% of males and 40% of females said they regularly attend concerts.

⇒Total number of males that attend the concert = 45% × 51 x

=
`(45)/(100)` × 51 x = 22.95 x

⇒Total number of males that attend the concert = 22.95 x

And

Total number of males that do not attend the concert = 51 x - 22.95 x

= 28.05 x

⇒Total number of males that do not attend the concert = 28.05 x

Also,

Total number of females that attend the concert = 40% × 49 x

=
`(40)/(100)` × 49 x = 19.6 x

⇒Total number of females that attend the concert = 19.6 x

And

Total number of females that do not attend the concert = 49 x - 19.6 x

= 29.4 x

⇒Total number of females that do not attend the concert = 29.4 x

(a)

The tree diagram is as follows :

(b)

Probability that a student is male and attends concert =
`(22.95 x)/(100 x)` × 100 %

= 22.95%

⇒Probability that a student is male and attends concert = 22.95%

(c)

Probability that a student is female and does not attend concert =
`(29.4x)/(100x)` × 100%

= 29.4%

⇒Probability that a student is female and does not attend concert = 29.4%

(d)

Probability that a student attends concerts =
`(22.95x + 19.6x)/(100x)` ×100%

=
`(42.55)/(100)` ×100%

= 42.55%

⇒Probability that a student attends concerts = 42.55%