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Find conditional probabilities

In an experiment, the probability that event AA occurs is 13\frac{1}{3}, the probability that event BB occurs is 79\frac{7}{9}, and the probability that events AA and BB both occur is 27\frac{2}{7}.\newlineWhat is the probability that AA occurs given that BB occurs?\newlineSimplify any fractions.\newline____\newline
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In an experiment, the probability that event AA occurs is 23\frac{2}{3}, the probability that event BB occurs is 13\frac{1}{3}, and the probability that events AA and BB both occur is 19\frac{1}{9}. What is the probability that AA occurs given that BB occurs? Simplify any fractions.
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Let h(x)=log⁡2(x)⋅x2 h(x)=\log _{2}(x) \cdot x^{2} .\newlineBelow is Jasmine's attempt to write a formal justification for the fact that the equation h(x)=3 h(x)=3 has a solution where 1≤x≤2 1 \leq x \leq 2 .\newlineIs Jasmine's justification complete?\newlineIf not, why?\newlineJasmine's justification:\newlineh(1)=0 h(1)=0 and\newlineh(2)=4 h(2)=4 , so 33 is between h(1) h(1) and h(2) h(2) .\newlineSo, according to the intermediate value theorem, h(x)=3 h(x)=3 must have a solution for an x x -value within the interval [1,2] [1,2] .\newlineChoose 11 answer:\newline(A) Yes, Jasmine's justification is complete.\newline(B) No, Jasmine didn't establish that 33 is between h(1) h(1) and h(2) h(2) .\newline(C) No, Jasmine didn't establish that h(x)=3 h(x)=3 22 is continuous.
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