Question

Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.3 and P(B) = 0.7. If an amount is zero, enter "0". What is P(A B)? What is P(A | B)? Is P(A | B) equal to P(A)? Are events A and B dependent or independent? A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate? What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

Answer 1

Answer:

See below

Step-by-step explanation:

What is P(A B)?

If A and B are mutually exclusive, then  

P(AB) = P(A∩B) = P(∅) = 0

What is P(A | B)?

By definition  

P(A | B) =  P(A∩B)/P(B).

Since  

P(A∩B) = 0, then P(A | B) = 0

Is P(A | B) equal to P(A)?

No, because P(A | B) = 0 and P(A) = 0.3

Are events A and B dependent or independent?

A and B would be independent if

P(A | B) = P(A) and P(B | A) = P(B)

But both P(A |B) and P(B | A) equals 0 and P(A) = 0.3, P(B) = 0.7

Hence, A and B are dependent.

A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?

No, it is not.

As we already saw, A and B are mutually exclusive but they are not independent.

What general conclusion would you make about mutually exclusive and independent events given the results of this problem?

If A and B are not empty events which are mutually exclusive, they can never be independent.