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.

Answer

`(i) 2/3 (ii) 1/5 (iii) 5/6`

Explanation

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`.