If the probability of an event occurring is p, then 1-p represents the probability of the same event not occurring. The value of p must lie between 0 and 1.
The probability that an event will occur plus the probability that it will not occur equals 1.
If the event in question is A and the probability of A occurring is P(A), then the probability of A not occurring is P(A')=1-P(A).
These events are complementary. Let P(A) = probability event will occur. Then the probability it will not occur is: 1 - P(A).
Probability can not be less than 0 or greater than 1. A probability of 0 means there is no possibility whatsoever of an event occurring. A probability of 1 means that the event is guaranteed to occur no matter what.
odds"The odds against an event is a ratio of the probability that the event will fail to occur (failure) to the probability that the event will occur (success). To find odds you must first know or determine the probability of success and the probability of failure.Odds against event = P(event fails to occur)/P(event occurs) = P(failure)/P(success)The odds in favor of an event are expressed as a ratio of the probability that the event will occur to the probability that the event will fail to occur.Odds in favor of event = P(event occurs)/P(event fails to occur) = P(success)/P(failure)"Allen R. Angel, Christine D. Abbott, Dennis C. Runde. A Survey of Mathematics with Applications. Pearson Custom Publishing 2009. Pages 286-288.
The probability that an event will occur plus the probability that it will not occur equals 1.
If the event in question is A and the probability of A occurring is P(A), then the probability of A not occurring is P(A')=1-P(A).
These events are complementary. Let P(A) = probability event will occur. Then the probability it will not occur is: 1 - P(A).
"Odds".
Odds.
The complement of an event occurring is that it does not occur.
p/(1-p) the relation between both outcomes.
odds
Probability can not be less than 0 or greater than 1. A probability of 0 means there is no possibility whatsoever of an event occurring. A probability of 1 means that the event is guaranteed to occur no matter what.
Let p = probability the event will occur; and q = probability the event will not occur. The relationship is p=1-q or q=1-p.
If the event is truly impossible, it has a zero probability of occurring. The definition of impossible is "not able to occur, exist, or be done," so that means there's no chance of it happening.
odds"The odds against an event is a ratio of the probability that the event will fail to occur (failure) to the probability that the event will occur (success). To find odds you must first know or determine the probability of success and the probability of failure.Odds against event = P(event fails to occur)/P(event occurs) = P(failure)/P(success)The odds in favor of an event are expressed as a ratio of the probability that the event will occur to the probability that the event will fail to occur.Odds in favor of event = P(event occurs)/P(event fails to occur) = P(success)/P(failure)"Allen R. Angel, Christine D. Abbott, Dennis C. Runde. A Survey of Mathematics with Applications. Pearson Custom Publishing 2009. Pages 286-288.