Question 570955
a)

Two events A and B are mutually exclusive when P(A or B) = P(A) + P(B). 


So let's plug in the given values to see if that's indeed true.



P(A or B) = P(A) + P(B)


1/2 = 1/3 + 1/3


1/2 = 2/3



This is false, so the events are NOT mutually exclusive

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b)

The formula given above really expands to 


P(A or B) = P(A) + P(B) - P(A & B)


and you can solve for P(A & B) to get


P(A & B) = P(A) + P(B) - P(A or B)

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So plug in the given values to get...


P(A & B) = P(A) + P(B) - P(A or B)


P(A & B) = 1/3 + 1/3 - 1/2


P(A & B) = 2/3 - 1/2


P(A & B) = 4/6 - 3/6


P(A & B) = 1/6