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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 I. 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 ſail, 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.
