csat-suneung 2013 Q8

csat-suneung · South-Korea · csat__math-humanities 3 marks Conditional Probability Direct Conditional Probability Computation from Definitions

For two events $A, B$, $$\mathrm{P}(A \cap B) = \frac{1}{8}, \quad \mathrm{P}\left(B^{C} \mid A\right) = 2\mathrm{P}(B \mid A)$$ what is the value of $\mathrm{P}(A)$? (Here, $B^{C}$ is the complement of $B$.) [3 points]
(1) $\frac{5}{12}$
(2) $\frac{3}{8}$
(3) $\frac{1}{3}$
(4) $\frac{7}{24}$
(5) $\frac{1}{4}$

For two events $A, B$,
$$\mathrm{P}(A \cap B) = \frac{1}{8}, \quad \mathrm{P}\left(B^{C} \mid A\right) = 2\mathrm{P}(B \mid A)$$
what is the value of $\mathrm{P}(A)$? (Here, $B^{C}$ is the complement of $B$.) [3 points]\\
(1) $\frac{5}{12}$\\
(2) $\frac{3}{8}$\\
(3) $\frac{1}{3}$\\
(4) $\frac{7}{24}$\\
(5) $\frac{1}{4}$

Paper Questions

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