Question

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

(i) a two-digit number  (ii) a perfect square number  (iii) a number divisible by 5.

Answer 1

(i) Number of two digit numbers \(=90-(1,2,3,4,5,6,7,8,9)=81\)
\(P(\) a two-digit number \()=81 / 90\)
(ii) Number of perfect squares \(=1,4,9,16,25,36,49,64,81=9\)
\(\mathrm{P}(\) a perfect square number \()=9 / 90\)
(iii) Numbers divisible by \(5=5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80\), \(85,90=18\)
\(\mathrm{P}(\) a number divisible by 5\()=18 / 90\)