Question

Solve the following problem :

In a large school, 80% of the students like mathematics. A visitor asks each of 4 students, selected at random, whether they like mathematics.

Calculate the probabilities of obtaining an answer yes from all of the selected students.

Answer 1

Let X denote the number of pupils who like mathematics.

P(pupils like mathematics) = p = `(8)/(100) = (4)/(5)`   ...[Given]

q = 1 – p = `1 - (4)/(5) = (1)/(5)`

Given, n = 4

∴ X ~ B`(4, 4/5)`
The p.m.f. of X is given by

P(X = x) = `""^4"C"x 4/5^x  (1/5)^(4 - x), x` = 0, 1, ...,4

P(obtaining an answer yes form all of the selected students)
= P(X = 4)

= `""^4"C"_4 (4/5)^4 (1/5)^0`

= `(4^4)/(5^4)`

= `(256)/(5^4)`..