Question

A bag contains $5$ white and $7$ red balls. One ball is drawn at random. What is the probability that ball drawn is white?

Answer 1

Total no. of balls in the bag is $12$ $(7$ red and $5$ white$)$

No. of white balls in bag is $5$.

Therefore, ${}^5{C}_1$( Selecting $1$ out of $5$ items) times out of ${}^{12}{C}_1$( Selecting $1$ out of $12$ items) a white ball is picked.

Let $E$ be the event of drawing a white ball from the bag

We know that, Probability $P\left(E\right)$ $=\frac{\text{(No.of favorable outcomes)}}{\text{(Total no.of possible outcomes)}}$$=\frac{{}^5{C}_1}{{}^{12}{C}_1}$$=\frac{5}{12}$