Question

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is (i) not divisible by 3, (ii) a prime number greater that 7, (iii) not a perfect square number. Select the correct answer from above options

Answer 1

Correct Answer - (i) 2 3 (ii) 1 5 (iii) 5 6 Number of all possible outcomes = 30. (i) There are 10 numbers divisible by 3. Number of numbers not divisible by 3 = 30 - 10 = 20. ∴ P(getting a number not divisible by 3) = 20 30 = 2 3 . (ii) Prime numbers greater than 7 are 11,13,17,19,23,29. Number of these prime numbers = 6. ∴ P(getting a prime number greater than 7) = 6 30 = 1 5 . (iii) Perfect square numbers are 1,4,9,16,25. These are 5 in number. Number of those numbers which are not perfect squares = 30-5 = 25. ∴ P(getting non-perfect square numbers) = 25 30 = 5 6 .