Question

A group of 40 students from your school is part of the audience for a TV game show. The total number of people in the audience is 130. What is the theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots?

Answer 1

The theoretical probability of 3 students from your school being selected as contestants out of 9 possible contestant spots is 0.28

Step-by-step explanation:

School students = 40

Total people = 130

Total contestant spot = 9

Probability of 3 contestant from school = ?

The number of combinations of 3 of the 40 students getting a spot = ⁴⁰C₃

The number of combinations of the other audience members filling the other 6 spots = ⁹⁰C₆

The number of 9 contestants with 3 students in them = ⁴⁰C₃ X ⁹⁰C₆

The total number of possible 9 contestants from the audience = ¹³⁰C₉

Probability of the group of contestants having 3 students =
`(^4^0C_3 X ^9^0C_6)/(^1^3^0C_9)`

Solving the equation further we get:

Probability of the group of contestants having 3 students = 0.28