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If (apple, 1/2; orange, 1/2) (apple, 1/4; orange, 3/4) (apple, 1/8; orange, 7/8) then the continuity axiom says that the exists a probability p such

If

(apple, 1/2; orange, 1/2) (apple, 1/4; orange, 3/4) (apple, 1/8; orange, 7/8)

then the continuity axiom says that the exists a probability p such that

(apple, 1/4; orange, 3/4) p(apple, 1/2; orange, 1/2) + (1 p)(apple, 1/8; orange, 7/8)

What would the value of p be in this case?

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