Question

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears

(i) a two-digit number 

(ii) a perfect square number

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Answer 1

Answer:

ANSWER

Solution(i):

Let E be the event of drawing a disc from the box of discs numbered from 1 to 90

Two digit numbers from 1 to 90=10,11,12,.....,90

No. of favorable outcomes=81

Total no. of possible outcomes =90

We know that, Probability P(E) =(Total no.of possible outcomes)(No.of favorable outcomes)=9081=109

Therefore, the probability of a two digit numbered disc from the box of discs numbered from 1 to 90=109

Solution(ii):

Let F be the event of drawing a perfect square numbered disc from the box of discs numbered from 1 to 90

Perfect square numbers from 1 to 90=1,4,9,16,25,36,49,64,81

No. of favorable outcomes=9

Total no. of possible outcomes =90

We know that, Probability P(F) =(Total no.of possible outcomes)(No.of favorable outcomes)=909=101

Therefore, the probability of drawing a perfect square numbered disc from the box of discs numbered from 1 to 90=101

Solution(iii):

Let G be the event of drawing a disc with a number divisible by 5 from the box of discs numbered from 1 to 90

Numbers divisible by 5 from 1 to 90=5,10,15,20,25,30,35,40,45,50,55,60,65,