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

Concept: Probability of an event: \[ P(E) = \frac{\text{Favourable outcomes}}{\text{Total outcomes}} \]
Step 1: Total number of balls. \[ 5 + 8 + 7 = 20 \]
Step 2: Meaning of “neither red nor black”. This means the ball must be
white. Number of white balls = 8
Step 3: Find probability. \[ P(\text{white}) = \frac{8}{20} \]
Step 4: Simplify. \[ \frac{8}{20} = \frac{2}{5} \]
Conclusion: The probability that the ball drawn is neither red nor black is $\frac{2}{5}$.