Question

A box contains 6 pens, 12 of which are defective. Two pens are taken randomly from the box. If r.v. X : number of defective pens obtained, then standard deviation of X = ______.

Options

• `± 4/(3sqrt(5))`

• `8/3`

• `16/45`

• `4/(3sqrt(5))`

Answer 1

A box contains 6 pens, 12 of which are defective. Two pens are taken randomly from the box. If r.v. X : number of defective pens obtained, then standard deviation of X = `underlinebb(4/(3sqrt(5)))`.

Explanation:

Given, X is the number of defective pens obtained. Two pens are defective.

So, X has possible values 0, 1, 2

Now, P(X = 0) = `(""^4C_2)/(""^6C_2) = (4 xx 3)/(6 xx 5) = 6/15`

P(X = 1) = `(""^2C_1 xx ""^4C_1)/(""^6C_2) = 8/15`

P(X = 2) = `(""^2C_2)/(""^6C_2) = (1 xx 2)/(6 xx 5) = 1/15`

E(X²) = `8/15 + 2^2/15 = 12/15 = 4/5`

Standard deviation = `sqrt(E(X^2) - [E(X)]^2)`

= `sqrt((4/5) - (2/3)^2`

= `sqrt(16/45)`

= `4/(3sqrt(5))`