Probability
Independent Events
Premium Question
Grade 12
Question:
A problem in mathematics is given to three students $A, B, C$ whose probabilities of solving it are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that the problem is solved (by at least one of them) is:
(1) $\frac{1}{4}$
(2) $\frac{1}{2}$
(3) $\frac{3}{4}$
(4) $\frac{2}{3}$
Step-by-Step Solution
Key Concept: It is far simpler to first compute the probability that none of the three students solves the problem (treating their attempts as independent), and then subtract this from 1.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)