Question 382011
1. Consider an experiment of picking a ball twice in a box with 4 different balls numbering from 1 to 4. The picked ball in the first try should be returned to the box for the second try. 
1) Specify all the possible events from the experiment.
There are 4*4=16 possible events ranging from 1/1, to 4/4
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2) Find the probability of happening the event A, “the sum of the numbers from the two balls is 3”.
Events: 1/2, 2,2, 2/1
P(sum is 3) = 3/16
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3) Find the probability of happening the event B, “the number of the 2nd ball is 2”.
Events: 1/2,2/2,3/2,4/2
P(2nd ball is 2) = 4/16
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4) Find the probability of happening the event of A and B.
Event: 1/2 is in both event A and event B
P(A and B) = 1/16
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5) Find the probability of happening the event of A after the event B happens.
Event: P(sum is 3|2nd ball is 2) = 1/4
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6) Can we say that event A and B are mutually exclusive? If yes, why? or if not ,why not?
No, there is an element (1/2) that appears in both A and B.
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7) Can we say that event A and B are independent? If yes, why? or if not ,why not?
P(A|B) = 1/4
P(A)*P(B) = (3/16)(4/16) is not equal to P(A|B)
So A and B are not independent.
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Cheers,
Stan H.