Question

A bag contains $2$ green, $3$ red and $4$ black balls. A ball is taken out of the bag at random. Find the probability that the selected ball is not black.

Answer 1

Finding the probability that the selected ball is not black.

Let $\text{P}\left(\text{E}\right)$ be the probability that the selected ball is not black.

Total number of balls$=2\left(green\right)+3\left(red\right)+4\left(black\right)$

$=9$

$\therefore$Number of possible outcomes$=9$

Number of black balls$=4$

Number of balls other than black$=9-4$

$=5$

$\therefore$Number of favourable outcomes$=5$

We know that $\text{P}\left(\text{E}\right)$$=\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}$

So, $\text{P}\left(\text{E}\right)$$=\frac{5}{9}$

Hence, probability that the selected ball is not black$=\frac{\mathbf{5}}{\mathbf{9}}$