[Guest]

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

A scroll is 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, is entered on the scroll. On the day 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.

[Prof. Templeton]

But I would expect 90

[Guest]

But I would expect 90

Well, I may be thinking too much but I think

Shouldn't it be 91? The expected number of years is 90.6 and since he will die on his Xth birthday only, I think it should be 91.

However, going by that logic, if we round UP all the expected years, the expected age would be 100!

[Prof. Templeton]

Well, I may be thinking too much but I think

Shouldn't it be 91? The expected number of years is 90.6 and since he will die on his Xth birthday only, I think it should be 91.

However, going by that logic, if we round UP all the expected years, the expected age would be 100!

The expectation to collect all 24 letters would be 91 attempts. The first letter was entered on the day of his birth, so the second would be on his 1 year birthday and the 91st letter would be entered on his 90th birthday. That's how I thought about it.

[Guest]

ouch... my head hurts...