A bag contains 3 black balls, 4 white balls and 5 red balls.\nOne ball is drawn at random from the bag.\nWhat is the probability that the ball drawn is either white or red?

Introduction / Context:
This problem tests your understanding of basic probability with coloured balls in a bag. You need to identify the total number of equally likely outcomes and then count the favourable outcomes where the ball drawn is either white or red.

Given Data / Assumptions:

• Number of black balls = 3.
• Number of white balls = 4.
• Number of red balls = 5.
• One ball is drawn at random from the bag.
• The event of interest is that the ball is white or red.
• All balls are identical apart from their colour and each ball is equally likely to be drawn.

Concept / Approach:
Use the classical definition of probability: Probability = number of favourable outcomes / total number of outcomes. Here, favourable outcomes are balls that are white or red. We first compute the total number of balls, then the number that are white or red, and finally their ratio. We then express the answer as a decimal to match the options.

Step-by-Step Solution:
Total balls = 3 + 4 + 5 = 12 Number of white balls = 4 Number of red balls = 5 Favourable balls (white or red) = 4 + 5 = 9 Probability = favourable / total = 9 / 12 Simplify 9 / 12 = 3 / 4 = 0.75 Therefore the required probability is 0.75.

Verification / Alternative check:
We can also view the probability as one minus the probability of drawing a black ball. The probability of a black ball is 3 / 12 = 1 / 4 = 0.25. So the probability of not drawing black (that is, drawing white or red) is 1 - 0.25 = 0.75. This matches our main calculation.

Why Other Options Are Wrong:
Option 0.5 corresponds to 6 favourable balls out of 12, which does not match the actual 9 favourable balls. Option 0.25 is the probability of drawing a black ball, the complement of what we need. Option 0.8 would require 9.6 favourable outcomes out of 12, which is impossible for a discrete count of balls.

Common Pitfalls:
Students sometimes forget to include both colours in the favourable count or mistakenly divide by the number of colours instead of the total number of balls. Another mistake is to misread the question and include black balls as well. Always recheck the total number of balls and the exact event described in the wording.

Final Answer:
The probability that the ball drawn is either white or red is 0.75.