Question

A bag contains 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find
the probability that the ball drawn is not black.​

Answer 1

Black balls are represented by:

$B_1,B_2,B_3,B_4,B_5$

Red balls are represented by:

$R_1,R_2,R_3,R_4,R_5,R_6,R_7$

And white balls are represented by:

$W_1,W_2,W_3$

Let S be the sample space of the possible ways of drawing a ball,

$S=ways\:of\:choosing\:one\:ball\\=\{B_1,B_2,B_3,B_4,B_5,R_1,R_2,R_3,R_4,R_5,R_6,R_7,W_1,W_2,W_3\}\\\implies n(S) = 5+7+3=15$

A be the event where the ball drawn is black

$\implies A=\{B_1,B_2,B_3,B_4,B_5\}\\\implies n(A) = 5$

Then, the event where the ball drawn is not black is (S-A)

$P(S-A) = \frac{n(S-A)}{n(S)} \\=\frac{n(S)-n(S\cap A)}{n(S)}\\=\frac{15-n(A)}{15}\:\:\:\:[A\subseteq S \implies S\cap A = A]\\\\=\frac{15-5}{15}=\frac{10}{15}=\frac{2}{3}$

Hence probability that the ball drawn is not black is 2/3