Question

Cards numbered 1 to 30 are put in a bag. A card is drawn at random from this bag. Find the probability that the number on the drawn card is

 (i) not divisible by 3 

(ii) a prime number greater than 7 

(iii) not a perfect square number.

Answer 1

Total number of possible outcomes, n(S) = 30 

(i) Number of favorable outcomes of numbers divisible by 3, 

n(E) = 10

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{10}{30}\) = \(\frac{1}{3}\)

Probability of getting a number not divisible by 3 = 1 – P(E)

= 1 - \(\frac{1}{3}\) = \(\frac{2}{3}\)

(ii) Number of favorable outcomes, 

n(E) = 6

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{6}{30}\) = \(\frac{1}{5}\)

(iii) Number of favorable outcomes of getting a perfect square, 

n(E) = 5

 = 1 - \(\frac{1}{6}\) = \(\frac{5}{6}\)