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Cards with numbers 1, 2, 3, ........... 100 are placed in a box and mixed thoroughly. One card is drawn. What is the probability that the card drawn is

(i) a prime number less than 30?

(ii) a multiple of 5 and 7? 

(iii) a multiple of 5 or 7?

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1 Answer

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(i) Favourable cards are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, i.e., 10.

P (prime number less than 30) = 10/100 or 1/10

(ii) Favourable cards are 35, 70. 

(card is a multiple of 5 and 7) = 2/100 or 1/50

(iii) Favourable cards are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 7,14, 21, 28, 42, 49, 56, 63, 77, 84, 91, 98 i.e., 32 P(card is a multiple of 5 or 7) = 32/100  or 8/25.

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