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) an even number
(iii) a number divisible by 3.

Answer 1

Total number of possible outcomes$=19$
(i) The prime numbers between 1 and 19 are 2, 3, 5, 7, 11, 13, 17 and 19.
Total number of primes $=8$
∴ ${\mathrm{P}}_{\left(\mathrm{prime}\mathrm{number}\right)}=\frac{8}{19}$

(ii) The even numbers between 1 and 19 are 2, 4, 6, 8, 10 ,12, 14, 16 and 18.

Total number of even numbers$=6$
∴ ${\mathrm{P}}_{\left(\mathrm{even}\mathrm{number}\right)}=\frac{9}{19}$

(iii) The numbers between 1 and 19 which are divisible by 3 are 3, 6, 9, 12, 15 and 18.
Total number of possible outcomes = 6
∴ ${\mathrm{P}}_{\left(\mathrm{number}\mathrm{divisble}\mathrm{by}3\right)}=\frac{6}{19}$