Question

In a box of floppy discs, it is known that 95% will work. A sample of three of the discs is selected at random. Find the probability that exactly one floppy disc work.

Answer 1

Let X = number of working discs.

p = probability that a floppy disc works

∴ p = 95% = `95/100 = 19/20`

and q = 1 - p = `1 - 19/20 = 1/20`

Given: n = 3

∴ X ~ B`(3, 19/20)`

The p.m.f. of X is given by

P(X = x) = `"^nC_x  p^x q^(n - x)`

i.e. p(x) = `"^3C_x (19/20)^x (1/20)^(3-x)`, x = 0, 1, 2, 3

P(exactly one floppy discs work) = P(X = 1)

= p(1) = `"^3C_1 (19/20)^1 (1/20)^(3 - 1)`

`= 3 xx 19/20 xx (1/20)^2`

`= 3(19/20^3)`

Hence, the probability that none of the floppy disc will work = 3`(19/20^3)`