in que 8.7 we have the case where the probability that a butterfly will die on day on day 3 is 0.25 whereas the probability of a butterfly dying on day 3 given they were alive at the start of day 3 is 0.417. But surely in order to die they have to be alive at the start of the day don't they? So I am missing the difference - thanks.
Without having the question in front of me, the difference appears to be that in one death is possible on days one or two - whereas in the other you know that can't have happened.
But surely you can only die once so if we are saying P(X=3)=0.25 then doesn't that mean X cant have equaled 1 or 2? And therefore P(X=3)=P(X=3|X>=3)?
No, the amount of information you have in each case is different, at the point you are judgi8ng the probability. Scenario one Day 1: might die Day 2: might die Day 3: might die Day 4: might die Day 5: might die Scenario two Day 1: didn't die Day 2: didn't die Day 3: might die Day 4: might die Day 5: might die Whatever the probabilities assigned to each day, it should be obvious that the situations are not the same.
Got it - say in case 2, at day 3 because there was no chance of having died previously, the probability is much higher.
