Topic: Electronics Engineering
A man with n keys wants open a lock. He tries his keys at random. The expected number of attempts for his success is (keys are replaced after every attempt)
- A. $n/2$
- B. n
- C. $\sqrt{n}$
- D. None of the above
Answer: B. n
Explanation: $E(x)=\Sigma xP(x) = 1\times\frac{1}{n}+2(\frac{n-1}{n})\times\frac{1}{n}+3(\frac{n-1}{n})^{2}\times\frac{1}{n}\cdot\cdot\cdot = n$