topic02 - Topic 2 Probability 2.1 Probability A probability...

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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.
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