(I) a two-digit number

(ii) an ideal square number

(iii) a number distinguishable by 5.

Solution:

The complete number of plates = 90

P(E) = (Number of great results/Total number of results)

(I) Total number of plates having two digit numbers = 81

(Since 1 to 9 are single digit numbers thus, complete 2 digit numbers are 90-9 = 81)

P (bearing a two-digit number) = 81/90 = 9/10 = 0.9

(ii) Total number of amazing square numbers = 9 (1, 4, 9, 16, 25, 36, 49, 64 and 81)

P (getting an ideal square number) = 9/90 = 1/10 = 0.1

(iii) Total numbers which are separable by 5 = 18 (5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85 and 90)

P (getting a number separable by 5) = 18/90 = ⅕ = 0.2