Question

In: Statistics and Probability

True or False? When using calculator function key, please indicate what key was used. A correct...

True or False? When using calculator function key, please indicate what key was used. A correct answer without any justification may receive no credit.

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

Solutions

Expert Solution

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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orchestra answered 1 year ago

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