Trivia

Subject:
Re: Correct!
Response To:
Correct! ()

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?

© 1998 - 2017 by Ellis Walentine. All rights reserved.
No parts of this web site may be reproduced in any form or by
any means without the written permission of the publisher.

WOODCENTRAL, P.O. BOX 493, SPRINGTOWN, PA 18081