SOLUTION: suppose A and b are events such that P(A)=1/3, P(B)= 1/3, and P(Aor B)=1/2. complete parts (a) and (b) below. a. are events A and B mutually exclusive ? explain your answer. b. d

Algebra ->  Probability-and-statistics -> SOLUTION: suppose A and b are events such that P(A)=1/3, P(B)= 1/3, and P(Aor B)=1/2. complete parts (a) and (b) below. a. are events A and B mutually exclusive ? explain your answer. b. d      Log On


   

Question 570955: suppose A and b are events such that P(A)=1/3, P(B)= 1/3, and P(Aor B)=1/2. complete parts (a) and (b) below.
a. are events A and B mutually exclusive ? explain your answer.
b. determine P(A &B).
P(A& B) = ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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