7B And Probability: Independent Events

And Probability Dependent Events

Two events are dependent if the outcome of one even affects the probability of the other event.

And Probability Independent Events

Two events are independent if the occurrence of one event does not affect the probability of the other event.

Either/Or Porbability: Non-overlapping Events

Two events are non-overlapping if they cannot occur together.

Either/Or Probability: Overlapping Events

Two events are overlapping if they can occur together.

Formula

If A and B are non-overlapping events, the probability that either A or B occurs is P(A and B)= P(A) + P(B)

Formula

If A and B are overlapping events, the probability that either A or B occurs is P(A and B) =P(A) + P(B) -P(A and B)

Formula

Consider two independent events A and B with individual probabilities P(A) and P(B). THe and probability that A and B both occur is P(A and P)=P(A)xP(B). Can be extended over any number of events.

At least once Rule for independent events

Suppose the probability of an event A occuring in one trial is P(A). If all trials are independent, the probabiliyt that event A occurs at least on in n trials is P(at least one event A in n trials) = 1- [P(no events A in trials)] to the nth power

Formula

The and probability that dependent events A and B occurs is P(A and B)=P(A)xP(B given A). (P of b given A: The probability of event B given the occurrence of Event A.)Can be extended over any number of events.