Question

In a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3.

The roll numbers of students begin with boys and end with girls. Find the probability
that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number.​

Answer 1

The probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number is
`(4)/(7)` .

Explanation:

We are given that in a class of 35, students are numbered from 1 to 35. The ratio of boys to girls is 4:3.

The roll numbers of students begin with boys and end with girls.

Firstly, we will calculate the number of boys and girls in the class.

Number of boys in the class =
`(4)/(7)* 35`

=
`4 * 5` = 20

Number of girls in the class =
`(3)/(7)* 35`

=
`3 * 5` = 15

So, the roll numbers of boys are numbered as = {1, 2, 3,..........., 19, 20}

and the roll numbers of girls are numbered as = {21, 22, 23,..........., 34, 35}

Prime numbers are those numbers that come in their own tables and 1.

The roll number of boys having prime numbers are = {2, 3, 5, 7, 11, 13, 17, and 19}

There are total of 8 boys.

Composite numbers are those numbers that come in the tables of other numbers also.

The number of girls with composite roll number or an even roll number = {21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, and 35}

There are a total of 12 girls.

So, the total number of favorable boys and girls = 8 + 12 = 20

Total number of students in class = 35

So, the probability that a student selected is either a boy with prime roll number or a girl with composite roll number or an even roll number is given by =
`(20)/(35)` =
`(4)/(7)` .