A bag contains 3 red, 4 white, and 7 black balls (14 total). If one ball is drawn at random, what is the probability that it is red or black?

Introduction / Context:
The probability of a union of disjoint simple events (red or black) equals the sum of their individual probabilities because the events do not overlap on a single draw.

Given Data / Assumptions:

• Red = 3, White = 4, Black = 7, Total = 14.
• One random draw.

Concept / Approach:
P(red or black) = (red + black) / total = (3 + 7) / 14.

Step-by-Step Solution:
(3 + 7) / 14 = 10/14 = 5/7.

Verification / Alternative check:
P(white) = 4/14 = 2/7; 5/7 + 2/7 = 1 as expected.

Why Other Options Are Wrong:
4/7 omits some favourable outcomes; 1/7 and 3/7 undercount severely.

Common Pitfalls:
Accidentally double-counting mutually exclusive colour events (not applicable on a single draw).

Final Answer:
5/7