Statistics Chapter 5
Basic Rules of Probability -✅✅ --The probability of any event is a number between
0 and 1.
-All possible outcomes together must have probabilities whose sum is 1.
-If all outcomes in the sample space are equally likely, the probability that event A
occurs can be found using the formula:
P(A)=(number of outcomes corresponding to event A)/(total number of outcomes in
sample space)
-The probability that an event does not occur is 1 minus the probability that the event
does occur.
-If two events have no outcomes in common, the probability that one or the other
occurs is the sum of their individual probabilities.
Complement - ✅✅-We refer to the event "not A" as the complement of A.
Conditional Probability - ✅✅-The probability that one event happens given that
another event is already known to have happened is called a conditional probability.
Suppose we know that event A had happened. Then the probability that event B
happens given that event A has happened is denoted by P(B|A).
Event - ✅✅ -An event is any collection of outcomes from some chance process.
That is, an event is a subset of the sample space. Events are usually designated by
capital letters, like A, B, C, and so on. If A is an event, we write its probability as
P(A).
False Positives, False Negatives - ✅✅ -If the condition being tested is uncommon
in the population, many positives will be false positives.
General Addition Rule - ✅✅-P(A∪B)=P(A)+P(B)-P(A∩B)
General Multiplication Rule - ✅✅-The probability that events A and B both occur
can be found using the general multiplication rule P(A∩B)=P(A)*P(B|A) where P(B|A)
is the conditional probability that event B occurs given that event A has already
occurred.
Independent Events - ✅✅ -Two events are independent if the occurrence of one
event has no effect on the chance that the other event will happen. In other words,
events A and B are independent if P(A|B)=P(A) and P(B|A)=P(B). Two mutually
exclusive events can never be independent, because if one event happens, the other
event is guaranteed not to happen.
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