Question 465430
Suppose A and B are events with P(A) = 1/4, P(B) = 2/5, and P(A or B) = 1/2. 
a) Are the events A and B mutually exclusive? Explain your reasoning.
no as you can see in the answer to "b" (below).
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b) What is P(A and B) 
= P(A) + P(B) - P(A or B)
= (1/4) + (2/5) - (1/2) 
= (13/20)- (10/20) = 3/20
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c) Are the events A and B independent? 
Check: P(A)*P(B) = P(A|B) ???
(1/4)(2/5) = P(A and B)/P(B)  ???
2/20 = (3/20)/(2/5) ???
1/10 = 6/100 ??? 
Answer: 1/10 does not equal 3/50
So A and B are not independent.
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Cheers,
Stan H.