Question 588334
P(A and B) = P(A) + P(B) - P(A or B)


P(A and B) = 8/10 + 9/10 - x


P(A and B) = 17/10 - x


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P(A | B) = P(A and B)/P(B)


P(A | B) = (17/10 - x)/(9/10)



Since  0 < P(A or B) < 1, this means that the smallest value of x is x = 0 and the largest value of P(A | B) is P(A | B) = (17/10 - 0)/(9/10) = 17/9


and the largest value is x = 1, so the smallest value of P(A | B) = (17/10 - x)/(9/10) is P(A | B) = (17/10 - 1)/(9/10) = 7/9



Note: the largest and smallest are mixed up because if you have something like 1-x (where 0 < x < 1), then as x increases 1-x decreases (and vice versa). Similar reasoning applies when x decreases.



Therefore, if P(A) = 8/10 and P(B) = 9/10, then  P(A|B) is greater than or equal to 7/9.