Question

There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

• A. $\frac{11}{18}$
• B. $\frac{7}{18}$
• C. $\frac{2}{3}$
• D. $\frac{5}{18}$

Answer 1

The correct option is A

$\frac{11}{18}$

Given,
Number of green balls = 5
Number of black balls = 6
Number of white balls = 7
Total number of outcomes = 5 + 6 + 7 = 18
There are 18 balls out of which 11 are not white.
$\Rightarrow$ Number of favourable outcomes = 11

$\text{Probability of an event, P(E)}=\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}$
$\Rightarrow$ P( ball drawn is not white) = $\frac{11}{18}$

$\therefore$ Probability that the ball drawn is not white is $\frac{11}{18}$ .

Alternate Method:
P (ball drawn is white) = $\frac{7}{18}$
By complementary event formula,
P( ball drawn is white) + P( ball drawn is not white) = 1
$\Rightarrow$ P( ball drawn is not white)
$=1-\text{P( ball drawn is white)}$
$=1-\frac{7}{18}=\frac{11}{18}$
$\therefore$ Probability that the ball drawn is not white is $\frac{11}{18}$.