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.

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.

1. A
$\frac{4}{15}$
2. B
$\frac{1}{15}$
3. C
$\frac{2}{3}$
4. D
$\frac{7}{15}$

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Solution:

Given: Number of red balls $=7$.
Number of white balls $=3$.
Number of black balls $=5$.
The total number of outcomes $n\left(S\right)=7+3+5$
$⇒n\left(S\right)=15$ Let A is an event of drawing a ball that is not black. So it can be white or red balls.
Number of favourable outcomes, $n\left(A\right)=7+3$
$⇒n\left(A\right)=10$

$P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}$
$⇒P\left(A\right)=\frac{10}{15}$
$⇒P\left(A\right)=\frac{2}{3}$
The probability that the ball drawn is not black is $\frac{2}{3}$.
Here, the correct option is 3.

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