Question

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is not a multiple of 6?

Answer 1

Clearly, the sample space is given by S = {1, 2, 3, 4, 5........19, 20}.
i.e. n(S) = 20

Let E₆ = event of getting a number which is not a multiple of 6
Then E₆' = event of getting a number which is a multiple of 6
E₆' = {6, 12, 18}
i.e. n(E₆' ) = 3
Now, P(E₆') = \[\frac{3}{20}\]

Hence, required probability P(E₆) = 1 − P(E₆')

                                                     = \[1 - \frac{3}{20} = \frac{20 - 3}{20} = \frac{17}{20}\]