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 

(i) none 

(ii) 1 

(iii) 2 

(iv) all 3 of the sample will work.

Answer 1

Let X = number of working discs. 

p = probability that a floppy disc works

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

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

Hence, the probability that none of the floppy disc will work = 1/20³.

(ii) P(exactly one floppy disc works) = P(X = 1)

Hence, the probability that exactly one floppy disc works = 3(19/20³)

(iii) P(exactly two floppy discs work) = P(X = 2)

Hence, the probability that exactly 2 floppy discs work = 3(19³/20³)

(iv) P(all 3 floppy discs work) = P(X = 3)

Hence, the probability that all 3 floppy discs work = (19/20)³.