Page:Philosophical Transactions - Volume 053.djvu/442

 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 ingle trial lies omewhere between any two degrees of probability that can be named.

SECTION I.

DEFINITION I. Several events are inconitent, when if one of them happens, none of the ret can.

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

3. An event is aid to ail, when it cannot happen; or, which comes to the ame thing, when its contrary has happened. 4. An event is aid 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 ame as probability.

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

PROP. I.

When everal events are inconitent the probability of the happening of one or other of them is the um of the probabilities of each of them.