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Question

(i) 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. [CBSE 2011]
(ii) 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) a two-digit number
(b) a number divisible by 5 [CBSE 2017]

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Solution

(i)
Total number of outcomes = 80.

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

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

Thus, number of favourable outcomes = 8.

∴ P(getting a perfect square number) = P(E1) = Number of outcomes favourable to E1Number of all possible outcomes
= 880=110

Thus, the probability that the disc bears a perfect square number is 110.

(ii)
Total possible outcomes = 90.
(a) Two-digit numbers are 10,11,12,13...90.
P(getting a two-digit number)=8190=910.

(b) Numbers divisible by 5 are 5,10,15,20...90.
P(number divisible by 5)=1890=15.

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