In a fairy tale, the fairy grandmother has assured the queen that her yet unborn baby prince will not die until the following set of conditions is fulfilled.

A scroll shall be prepared, and on the day of the birth and every subsequent birthday, a letter of the Greek alphabet from Α to Ω inclusively, chosen at random with replacement, shall be entered on the scroll. On the day that all the 24 distinct letters from Α to Ω of the alphabet appears, the prince will die.

Determine the expectation of the prince's life in years.

(In reply to Fenceposts? Beta test version by ed bottemiller)

Yes, the solutions given do account for the fact that the first letter is "awarded" at birth. In Charlie's solution, he counts down from 23 letters remaining, to 1 letter remaining, and adds the expected number of years it should take before one of the remaining letters is chosen (T=T+24/I).

Had he started at 24 letters remaining, and counted down from there, the solution would have been off by 1 year as you've indicated.

Posted by Justin on 2009-12-10 21:31:28