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Question

A box contains 100 cards marked with number 1 to 100. If one card is drawn randomly from the box.Find the probability that it bears.
(1) Even prime number
(2) A number divisible by 7
(3) The number at unit place is 9.

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Solution

Total number of outcome =100
Prime numbers from 1 to 100 are
2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97
Total number of cards with even prime numbers =1=x
Numbers divisible by 7 from 1 to 100 are
7,14,21,28,35,42,47,56,63,70,77,84,91,98
Total number of cards divisible by 7=14=y
Numbers with 9 at units place from 1 to 100 are
9,19,29,39,49,59,69,79,89,99
Total number of cards with 9 at units place =10=z

1) Probability of an even number =Total number of cards with even numberTotal outcomes=x100=1100=0.01

2) Probability of number divisible by 7 =Total number of cards with number divisible by 7Total outcomes=y100=14100

3) Probability of number having 9 at units place =Total number of cards with 9 at units placeTotal outcomes=z100=10100

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