To solve this problem, we need to find the probability of each given event.
Given:
There are 30 cards numbered from 1 to 30 in the bag.
(i) Probability that the number on the drawn card is not divisible by 3:
Total number of cards = 30
Number of cards not divisible by 3 = 20 (1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 20, 22, 23, 25, 26, 28, 29)
Probability = Number of cards not divisible by 3 / Total number of cards
Probability = 20 / 30 = 2/3
(ii) Probability that the number on the drawn card is a prime number greater than 7:
Prime numbers greater than 7 in the range of 1 to 30 are: 11, 13, 17, 19, 23, 29
Number of prime numbers greater than 7 = 6
Probability = Number of prime numbers greater than 7 / Total number of cards
Probability = 6 / 30 = 1/5
(iii) Probability that the number on the drawn card is not a perfect square number:
Perfect square numbers in the range of 1 to 30 are: 1, 4, 9, 16, 25
Number of cards that are not perfect square numbers = 25
Probability = Number of cards that are not perfect square numbers / total number of cards
Probability = 25 / 30 = 5/6
Therefore, the probabilities are:
(i) Probability that the number on the drawn card is not divisible by 3 = 2/3
(ii) Probability that the number on the drawn card is a prime number greater than 7 = 1/5
(iii) Probability that the number on the drawn card is not a perfect square number = 5/6
