Probability
Classical Probability
Premium Question
Grade 12
Question:
Three letters are to be placed in three correctly addressed envelopes, one letter per envelope, at random. The probability that at least one letter is placed in its correctly addressed envelope is:
(1) $\frac{1}{3}$
(2) $\frac{2}{3}$
(3) $\frac{1}{6}$
(4) $\frac{5}{6}$
Step-by-Step Solution
Key Concept: It is easier to first find the probability that no letter goes into its correct envelope (a derangement of 3 objects), and then subtract this from 1.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)