Question

# A bag contains cards which are numbered from 2 to 90. A card is drawn at random from the bag. Find the probability that it bears(i) a two digit number (ii) a number which is a perfect square

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Solution

## Solution(i):Let E be the event of drawing a two digit number from the cards numbered from 2 to 90Two digit numbers from 2 to 90=10,11,12,.....,90No. of favorable outcomes=81Total no. of possible outcomes =89We know that, Probability P(E) =(No.of favorable outcomes)(Total no.of possible outcomes)=8189Therefore, the probability of a two digit number from the cards numbered from 2 to 90=8189Solution(ii):Let F be the event of drawing a perfect square number from the cards numbered from 2 to 90Perfect square numbers from 2 to 90=4,9,16,25,36,49,64,81No. of favorable outcomes=8Total no. of possible outcomes =89We know that, Probability P(F) =(No.of favorable outcomes)(Total no.of possible outcomes)=889Therefore, the probability of drawing a perfect square number from the cards numbered from 2 to 90=889

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