Question

A box contains 80 discs, which are numbered from 1 to 80. If one Disc is drawn at random from the box, find the probability that it bears a perfect square number.

Answer 1

The total number of outcomes = 80.

Let E₁ be the event of getting a perfect square number.

Out of these number perfect square number are 1, 4, 9, 16, 25, 36, 49, and 64.

Thus, the number of favorable outcomes = 8

Therefore, P(getting a perfect square number) = P(E₁) = \(\frac{number\, of \,outcomes\,favorable\,to\,E_1}{number\,of \,all\,possible\,outcomes} \) = \(\frac{8}{80}\) = \(\frac{1}{10}\).

Thus, the probability  tht the disc bears a perfect square number is \(\frac{1}{10}\).