## Trivia

Subject:
Re: Hint 3
Response To:
Hint 3 ()

Larry Barrett
The complete set of cases (using bold to indicate the event and italics to indicate the 'not x' event*) is ABC, ABC, BAC, CAB, ABC, ACB, BCA, ABC.
When observing for 2 hours, A is certain to erupt so the probability of all events which include A is 0, which eliminates all but four: ABC, ABC, ACB, ABC.

Alex has already shown us the probability for the ACB event occurring in a 2 hour period: 1*1/2*1/3= 1/6, and the probability that A occurs first is 1/2*1/6.
The probability of ABC occurring is 1*1/2*2/3 = 2/6, and the probability that A occurs first is 1*2/6.
The probability of ABC occurring is 1*1/2*2/3 = 2/6. and the probability that A occurs first is 1/2*2/6.
The probability of ABC occurring is 1*1/2*1/3 = 1/6, and the probability that A occurs first is 1/3*1/6.

So the probability that A occurs first in the 2 hour observation period is
1/2*1/6 + 1*2/6 + 1/2*2/6 + 1/3*1/6 = 3/36 + 12/36 + 6/36 + 2/36 = 23/36.
Similar calculations for the prob of B occurring first = 8/36 and for C occurring first = 5/36. The sum of all three probabilities is 23/36+8/36+5/36= 36/36= 1.

*My keyboard is configured so that the key which contains the 'not' symbol is used to toggle between the english and thai alphabets, so I needed another way to indicate the 'not x' event.