Q) A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a :
(i)   2-digit number less than 40
(ii)  number divisible by 5 and greater than 50
(iii) a perfect square number

Ans:

Total Number of discs = 90

∴ Total outcomes of drawing one disc = 90

(i) Probability of 2 digit number < 40:

In total, numbers < 40 are = 39

and in these numbers, there are single-digit numbers = 9

∴ 2 digits numbers < 40 = total numbers < 40 – total single digit numbers = 39 – 9 = 30

∴ Favorable outcomes of drawing a 2-digit number and < 40 = 30

∴ The probability of drawing a 2-digit number and < 40:

=

=

Therefore, the probability of a 2-digit number and < 40 is .

(ii) Probability of number divisible by 5 and > 50:

Since we need to take numbers> 50 and up to 90, these will be numbers from 51 to 90.

Now, between 51 and 90, Numbers divisible by 5 will be the numbers ending with ‘5’ and ending with ‘0’.

∴ numbers ending with 5 = 4                 (55, 65, 75, 85)

∴ numbers ending with 0 = 4                 (60, 70, 80, 90)

∴ Favorable outcomes of drawing a number divisible by 5 and > 50 = 4 + 4 = 8

∴ The probability of drawing a number divisible by 5 and > 50:

=

=

Therefore, the probability of a number divisible by 5 and > 50 is .

(iii) Probability of number being a perfect square number:

Between 1 and 90, perfect square numbers = 9

(i.e. 1, 4, 9, 16, 25, 36, 49, 64, 81)

∴ Favorable outcomes of drawing a perfect square number = 9

∴ The probability of drawing a perfect square number:

=

=

Therefore, the probability of the number being a perfect square is .

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