A box contains 90 discs which are number from 1 to 90 . If one disc is drawn at random form the box, find the probility that it bears:
(i) a two-digits number
(ii) a perfect square number
(iii) a numbre divisible by 5.

Explanation

Total number of disc in a box , n(s) = 90
(i) Let `E_(1)`= Evernt of selecting a two-digits number = `{10,11,......90}`
` " "n(E_(1)) = 81`
Probability of geting a two-digit number = `(n(E_(1)))/(n(E_(2))) = (81)/(90) = (9)/(10)`
(ii) Let `E_(2)` = Event of selecting a number divisibel by 5
`= { 5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90}`
`therefore " "n(E_(3)) = 18`
`therefore" "` Required probability `= (n(E_(3)))/(n(S)) = (2)/(6) =(1)/(3)`