Question

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn cards is 

(i) an odd number 

(ii) a perfect square number 

(iii) divisible by 5 

(iv) a prime number less than 20

Answer 1

Total number of possible outcomes, n(S) = 50 

(i) Number of favorable outcomes, 

n(E) = 25

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{25}{50}\) = \(\frac{1}{2}\)

(ii) Number of favorable outcomes, 

n(E) = 4

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{4}{50}\) = \(\frac{2}{25}\)

(iii) Number of favorable outcomes, 

n(E) = 10

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{10}{50}\) = \(\frac{1}{5}\)

(iv) Number of favorable outcomes, 

n(E) = 4

∴ P(E) = \(\frac{n(E)}{n(S)}\) = \(\frac{4}{50}\) = \(\frac{2}{25}\)