## Trivia

Larry Barrett

I do not only have a better explanation, I have some more questions about the results.

What bothers me is the possible dependence on the observation period of 2 hours. It seems to me that the result should not vary if you select a different observation period, but I am not sure of that. In any case, I repeated the calculations using an observation period of one hour. Now the probability of A occurring is 1/2, where it was 1 for the 2 hour period, and the probability of not A is also 1/2, so all eight cases are now in play.

I get the following result for someone watching for 1 hour:

Probability of seeing A first is 116/288

Probability of seeing B first is 50/288

Probability of seeing C first is 32/288

Probability of not seeing any is 90/288.

The sum of all four is 288/288, so it is likely that I did the calculations correctly, (but there could be compensation errors).

For the 2 hour observation, the results were 23/36, 8/36, 5/36, (and 0 for not seeing any eruption, since in that case A is certain to erupt in the 2 hour period).

Clearly the probabilities for the 1 hours observation period are lower for seeing A first, etc. but I think the non-zero 'no eruption' case should be eliminated. Doing this leaves the following:

Probability of seeing A first is 116/198 (=.59) which is less than 23/36 (=.64). Why are the two not equal?