Question

A box contains tickets numbered 1 to N. n tickets are drawn from the box with replacement. The probability that the largest number on the tickets is k is

• A.
• B. $\left( \frac { \mathrm { k } - 1 } { \mathrm {~N} } \right) ^ { \mathrm { n } }$
• C. 0
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let X denote the largest number on the n tickets drawn. We have P(X £ k) = and P(X £ k – 1) =

Thus P(X = k) = – $\left( \frac { \mathrm { k } - 1 } { \mathrm {~N} } \right) ^ { \mathrm { n } }$