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 Pí-} satisfies r(A, B,C)) = 2 PC,D,E, F) 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

a)

for in a sample space probability of all elements =1

thereofre P({A,B}}+P({C,D,E,F})=1

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

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

but as P({A,B,C}} =1/2 from above ; therefore P({C}) =0

b)

from above we have determinedP ({A,B}} =1/2

c)

as we have P ({A,B}} =1/2 which is one equation and there are two variable A and B ; hence we can not solve for B

therefore it is not possible to determine P({B,C})

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