By Jiruse M., Machek J.

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The general point is that drawing attention to the actions of an accused only strengthens the case against him if those actions are more likely when he is guilty that when he is innocent. If a bus journey took the accused past both the crime scene and the shopping centre he said he was visiting, then evidence that tended to prove he took that journey would not add to the case against him, as the two values of P(JourneYIInnocent) and P(JourneYIGuilty) would have the same value. 8 (Daniel Kahneman and Amos Tversky) In a given city, 85% of the taxicabs are Green, 15% are Blue.

The only escape is to accept that there can be subsets of n that do not qualify as events, to which probabilities can be attached. There you have it. It is not laziness, unwillingness to do more work than is strictly necessary, that makes us place restrictions on what can be events, it is mathematical necessity. 1 Conditional Probability If you throw a fair die, with no clues given about the outcome, the chance of getting a six is 1/6. But maybe you have been told that this blue die, and another red die were thrown, and their total score was four.

If the series is divergent, whatever the value of N, we can then choose M so that the sum exp( - N+M E n=N N+M E n=N P(An) is as large as we like, and hence the value of P(An)) is as small as we like. Hence P(BN) = 0, and so P(BN) = 1. 4, P ( P(C) = 1. e. D The Borel-Cantelli lemmas are an example of a so-called Zero-One Law: we have an event C that is either impossible, or it is certain. The second part of the theorem has the extra condition that the {An} are independent, and it is plain that some such condition will be required.