Question

A bag contains $10$ white, $5$ black, $3$ green and $2$ red balls. One ball is drawn at random. Find the probability that the ball drawn is white or black or green.

Answer 1

Let $W,B,G$ be the event of selecting a white, black, green ball respectively.
$n\left(S\right)=10+5+3+2=20$
$n\left(W\right)=10,n\left(B\right)=5,n\left(G\right)=3$
$P\left(W\right)=\frac{n\left(W\right)}{n\left(S\right)}=\frac{10}{20}$
$P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{5}{20}$
$P\left(G\right)=\frac{n\left(G\right)}{n\left(S\right)}=\frac{3}{20}$
Probabilities of getting white or black or green ball
$=P(W\cup B\cup G)$
$(W,B,G$ are mutually exclusive event)
$=P\left(W\right)+P\left(B\right)+P\left(G\right)$
$=\frac{10}{20}+\frac{5}{20}+\frac{3}{20}=\frac{18}{20}=\frac{9}{10}$