Question

15 cards numbered 1, 2, 3, 4,..., 14, 15 are put in a box and mixed thoroughly. A man draws a card at random from the box. Find the probability that the number on the card is
(i) an even number
(ii) a prime number
(iii) divisible by 3
(iv) divisible by 2 and 3

Answer 1

The possible outcomes are 1,2, 3,4, 5................15.
Number of all possible outcomes = 15

(i) Out of the given numbers, the even numbers are 2, 4, 6, 8, 10, 12 and 14.
Let E₁ be the event of getting an even number.
Then, number of favourable outcomes = 7​
∴ P (getting an even number) = $\frac{7}{15}$

(ii) Out of the given numbers, the prime numbers are 2, 3, 5, 7, 11 and 13.
Let E₂ be the event of getting a prime number.
Then,​ number of favourable outcomes =​ 6
∴ P (getting a prime number) = $\frac{6}{15}=\frac{2}{5}$

(iii) Out of the given numbers, the numbers divisible by 3 are 3, 6, 9, 12 and 15.
Let E₃ be the event of getting a number divisible by 3.

Then, ​number of favourable outcomes = 5
∴ P(getting a number divisible by 3) = $\frac{5}{15}=\frac{1}{3}$

(iv) Out of the given numbers, the numbers divisible by 2 and 3 are 6 and 12.

Let E₄ be the event of getting a number that is divisible by 2 and 3.
Then,​ number of favourable outcomes =​ 2
∴ P (getting a number divisible by 2 and 3) = $\frac{2}{15}$