In: Statistics and Probability
True or False? When using calculator function key, please indicate what key was used. A correct answer without any justification may receive no credit.
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a. ____________ For any event A, P(A) = 0 means A is certain to occur.
b. ____________ If P(B ) < P(A ), then event B is more likely to happen than event A.
c.____________ If P(A|B) = P(A ) then A and B are dependent.
d. ____________ If P(B|A) = P(B ) then A and B are independent.
e. ____________ If P(A and B) = P(A)P(B) then A and B are independent
f. ____________ P(A | B) = P(A and B)/P(A)
g. _______________ If P(A and B) = 0 then A and B are not mutually exclusive
a. Correct choice- False
Reason: P(A)=0 means that the event is not certain to occur and it is an impossible event.
b.Correct option- False
Reason: If the probabilty of a certain event say B is less than the probability of an event A,then it means that the event B is less likely to occur with respect to event A as higher the probability higher is the chances of that event happening and lesser the probability,lesser is the chance of the event happening.
c. Correct option- False
Reason:
:
and the above equation is possible if the events A and B are independent.
d. Correct option: True
Reason : If the events A and B are independent then,
e. Correct option : True
Reason: If ,
Then the events A and B are independent as the occurence of event A does not influence the occurence of event B as is clear because the probability of the two events occuring simultaneously is equal to the product of the probabilities of the two respective events.
f. Correct option: True
Reason: By the definition of conditional probability,
g. Correct option: False
Reason : By the definittion of mutually exclusive events, If A and B are two mutually exclusive events then they cant occur at the same time. In terms of probabilities,
which means that the events A and B are mutually exclusive .
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