Question 998749
I'll do the first part to get you started

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What is wrong with the following statements? Please explain. 
a.	P(A) = -0.3
b.	P(Ac)=0.6 given that P(A) = 0.3
c.	P(A or B) = 0.7 if P(A) =0.4 and P(B) =0.3
d.	P(A and B) is always greater than 0 

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a) 


You cannot have a negative probability. The probability MUST be between 0 and 1 (inclusive).


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b) 


P(A^c) + P(A) = 1 is always true. But notice how 0.6 and 0.3 do not add to 1. So we have a contradiction here. If P(A^c) = 0.6, then P(A) = 0.4. Or if P(A) = 0.3, then P(A^c) = 0.7


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c)


P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = P(A) + P(B) - P(A)*P(B) ... assuming A and B are independent
P(A or B) = 0.4 + 0.3 - 0.4*0.3
P(A or B) = 0.7 - 0.12
P(A or B) = 0.58


So P(A or B) should equal 0.58. P(A or B) is only equal to 0.7 IF events A and B are mutually exclusive. I.e. when P(A and B) = 0


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d)


The statement "P(A and B) is always greater than 0 " is false because it is possible for P(A and B) to be equal to zero. It is possible for events A and B to be mutually exclusive. Two events are mutually exclusive when they cannot happen at the same time.


Example:


Event A: Rolling a 5 on a single die
Event B: Rolling a 6 on a single die (same die as event A)