Question

A bag contains $6$ red, $8$ black and $4$ white balls. A ball is drawn at random. What is the probability that ball drawn is not black?

Answer 1

Total no. of balls in the bag is $18$ $(6-red,8-black,4-white)$

No. of balls that are not blackin bag is $10$ $(6$ red, $4$ white$)$

Therefore, ${}^{10}{C}_1$( Selecting $1$ out of $10$ items) times out of ${}^{18}{C}_1$( Selecting $1$ out of $18$ items) a ball that is not black is picked.

Let $E$ be the event of drawing a ball that is not black from bag

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^{10}{C}_1}{{}^{18}{C}_1}$$=\frac{10}{18}$$=\frac{5}{9}$