1.6 Probability spaces [10 pt] Consider a probability space where the sample spa

Question

1.6 Probability spaces [10 pt] Consider a probability space where the sample space is = {A,B,C,D,E, F and the event space is 2 Assume that we only know that the probability measure P satisfies r(A, B,C) 2 PC, D, E, Fl)- a) If possible, determine P(C), or show that such a probability cannot be determined unequivocally b) If possible, determine P(A, B), or show that such a probability cannot be determined unequivocally c) If possible, determine P(B,C), or show that such a probability cannot be determined unequivocally 2 points 2 points 6 points)

Explanation / Answer

ANSWER

a)

as we kow that sum of all probabilty in sample space =1

theefore P(A)+P(B)+P(C)+P(D)+P(E)+P(F) =1

here as P({A,B,C}) = P(A)+P(B)+P(C) =1/2

and P({C,D,E,F}) =P(C)+P(D)+P(E)+P(F) =1/2

adding above 2 equations:

P(A)+P(B)+P(C)+P(C)+P(D)+P(E)+P(F) =1/2+1/2

P(A)+P(B)+P(C)+P(D)+P(E)+P(F)+P(C) =1

1+P(C) =1

P(C)=0

b)

P({A,B,C})=P({A,B})+P(C) =1/2

P({A,B})+0 =1/2

P({A,B}) =1/2

c)P({B,C})=P(B)+P(C)=P(B)

here as from abvoe equation we have only equation P({A,B})+0 =1/2; and there are two variables therefore we can not solve for A and B.

hence we can not solve for P ( { B,C } )

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