SOLUTION: Suppose that a single fair die is rolled one time. Let events A and B be defined as: A = { 1, 4, 5 } and B = { 2, 4, 5, 6 } Are A and B mutually exclusi

Question 1168025: Suppose that a single fair die is rolled one time. Let events A and B be defined as:

A = { 1, 4, 5 } and B = { 2, 4, 5, 6 }

Are A and B mutually exclusive events? Why or why not?

Are A and B independent events? Show why or why not?
Please help me figure this out! On my last test, I had a similar question but with 3 digits and wrote independent and got it wrong!
Found 2 solutions by Boreal, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
No, because elements are common to both sets. If A were {1,2,3} and B were {4,5,6} then they would be.
P(A)*P(B)=P(Both A and B) if independent
1/2*2/3=1/3 if independent , and that is true.

Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

To learn this subject and to see many other similar solved problems, look into the lessons
    - Independent and mutually exclusive events
    - Dependent and independent events REVISITED
in this site.

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