Question

A bag contains 5 red, 8 white, and 7 black balls. A ball is drawn at random. Find the probability that the ball drawn is neither red nor black.

Hint:

“Neither A nor B” means choose outcomes excluding both — here only white balls.

Answer 1

Total Number of Balls
Red balls = 5
White balls = 8
Black balls = 7
Total balls = \(5 + 8 + 7 = 20\)

Event Required
The question asks for the probability that the ball drawn is neither red nor black.
This means the ball must be white.

Number of Favorable Outcomes
Number of white balls = 8

Probability Formula
\[ \text{Probability} = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values
\[ P(\text{white}) = \frac{8}{20} \] \[ P(\text{white}) = \frac{2}{5} \]
Final Answer
The probability that the ball drawn is neither red nor black is \(\frac{2}{5}\).