Question

in a box of floppy disc it is known that 95% will work. A sample of three of the disc is selected at random.Find the probability that all three of the sample will work​

Answer 1

Given:

In a box of floppy disc it is known that 95% will work.

A sample of three of the disc is selected at random.

To find:

Find the probability that all three of the sample will work​.

Solution:

Let the event that the disc works be represented by "W" and the event that the disc fails be represented by "F". Let the probability that  a disc will work is denoted by P(W) and the probability that a disc will fail is denoted by  P(F).

In a box of floppy disc it is known that 95% will work.

⇒ 95% = 95/100 = 0.95

Then P(W) = 0.95 and P(F) = 1 − P(W) = 1 − 0.95 = 0.05.

The probability that all 3 discs work is given by:

P(WWW) = P(W) × P(W) × P(W)  

= 0.95 × 0.95 × 0.95 = 0.95³ = 0.857375.