Question

A box contains 19 balls bearing numbers 1, 2, 3, ..., 19 respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is
(i) a prime number
(ii) divisible by 3 or 5
(iii) neither divisible by 5 nor by 10
(iv) an even number

Answer 1

The possible outcomes are 1,2, 3,4, 5................19.
Number of all possible outcomes = 19
(i) Out of the given numbers, the prime numbers are 2, 3, 5, 7,11,13,17,and 19.
Let E₁ be the event of getting a prime number.
Then, number of favourable outcomes = 8​
∴ P (getting a prime number) = $\frac{8}{19}$

(ii) Out of the given numbers, the numbers divisible by 3 are 3, 6, 9, 12, 15 and 18.

​ Out of the given numbers, the numbers divisible by 5 are 5,10 and 15.

Let E₂ be the event of getting a number divisible by 3 or 5.

Then,​ number of favourable outcomes = (6 + 3 − 1) = 8
∴ P (getting a number divisible by 3 or 5 ) = $\frac{8}{19}$

(iii) Out of the given numbers, the numbers divisible by 5 or by 10 are 5, 10, 15.
Let E₃ be the event of getting a number which is neither divisible by 5 nor by 10.
Then, number of favourable outcomes = 19 −3 = 16​
∴ P (getting a number which is neither divisible by 5 nor by 10) = $\frac{16}{19}$

(iv) Out of the given numbers , the even numbers are 2, 4, 6, 8, 10, 12, 14, 16 and 18.

Let E₄ be the event of getting an even number.
Then,​ number of favourable outcomes =​ 9
∴ P (getting an even number) = $\frac{9}{19}$