Question

A bag contains $4$ red, $5$ black and $6$ white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:

(i) white (ii) red (iii) not black (iv) red or white

Answer 1

Number of possible events $=n\left(S\right)=4+5+6=15$

(i) white

Let $A$ be the favourable events such that it is a white.

$\therefore P\left(A\right)=\frac{6}{15}=\frac{2}{5}$

(ii) red

Let $B$ be the favourable event such that it is red

$\therefore P\left(B\right)=\frac{4}{15}$

(iii) not black

not black is nothing but red or white.

Let $C$ be the favourable event such that it is not black.

$\therefore$ Number of favourable events $=N\left(C\right)=4+6=10$

$\therefore P\left(C\right)=\frac{10}{15}=\frac{2}{3}$

(iv) red or white

Let $C$ be the favourable event such that it is not black.

$\therefore$ Number of favourable events $=N\left(C\right)=4+6=10$

$\therefore P\left(C\right)=\frac{10}{15}=\frac{2}{3}$