Question

A box contains 19 balls bearing numbers 1, 2, 3…… 19. A ball is drawn at random from the box. What is the probability that the number on the ball is

a) a prime number

b) divisible by 3 or 5

Answer 1

The sample space is S = {1, 2, 3, …. 19}

n(S) = 19

a) Let E be the event of drawing a prime number.

E = {2, 3, 5, 7, 11, 13, 17, 19} ; n(E) = 8

P(E) = $\frac{n\left(E\right)}{n\left(S\right)}$= $\frac{8}{19}$

b) Let F be the event of drawing a number divisible by 3 or 5

F = {3, 5, 6, 9, 10, 12, 15, 18}; n(F) = 8

P(F) = $\frac{n\left(F\right)}{n\left(S\right)}$ =$\frac{8}{19}$