# 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 none of the floppy disc work. - Mathematics and Statistics

Sum

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 none of the floppy disc work.

#### Solution

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(none of the floppy discs work) = P(X = 0)

= p(0) = "^3C_0 (19/20)^0 (1/20)^(3 - 0)

= 1 xx 1 xx 1/20^3 = 1/20^3

Hence, the probability that none of the floppy disc will work = 1/20^3

Concept: Binomial Distribution
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