Topic 2 Probability
2.1 Probability
A probability is a measure of the likelihood that an event in the future will happen. Denote event by A ,
the probability of the event A by P(A) ,
1
)
(
0
≤
≤
A
P
, when P(A)=0 , we say A is an impossible event, P(A)=1, A is certain event .
2.2 Important Concepts
Experiment:
Observe some activity and take some measurement.
Outcome:
all possible results of an experiment.
Event :
the collection of one or more outcomes of an experiment
Mutually Exclusive Events
: the
occurrence of any one event means that none of the others can occur
at the same time. P(A and B)=0
Independent events
:the occurrence of one event does not affect the occurrence of another.
P(A and B) = P(A)*P(B)
Collectively exhaustive
: at least one of the events must occur when an experiment is conducted.
P(A or B)=1
.
Discuss these concepts based on the following example:
●
A fair die is rolled once.
–
Peter is concerned with whether the resulted number is even, i.e., 2, 4, 6.
–
Paul is concerned with whether the resulted number is less than or equal to 3, i.e., 1, 2, 3.
–
Mary is concerned with whether the resulted number is 6.
–
Sonia is concerned with whether the resulted number is odd, i.e., 1, 3, 5.
●
A fair die is rolled twice.
–
John is concerned with whether the resulted number of first roll is even, i.e., 2, 4, 6.
–
Sarah is concerned with whether the resulted number of second roll is even, i.e., 2, 4, 6.