Page:Philosophical Transactions - Volume 053.djvu/442

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PROBLEM.

Given the number of times in which an unknown event has happened and failed: Required the chance that the probability of its happening in a single trial lies somewhere between any two degrees of probability that can be named.

SECTION I.

Definition 1. Several events are inconsistent, when if one of them happens, none of the rest can.

2. Two events are contrary when one, or other of them must; and both together cannot happen.

3. An event is said to fail, when it cannot happen; or, which comes to the same thing, when its contrary has happened.

4. An event is said to be determined when it has either happened or failed.

5. The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon it's happening.

6. By chance I mean the same as probability.

7. Events are independent when the happening of any one of them does neither increase nor abate the probability of the rest.

PROP. I.

When several events are inconsistent the probability of the happening of one or other of them is the sum of the probabilities of each of them.

Suppose

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