csat-suneung 2009 Q26

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

For two events $A$ and $B$, $\mathrm { P } ( A ) = \frac { 1 } { 2 } , \mathrm { P } \left( B ^ { C } \right) = \frac { 2 } { 3 }$, and $\mathrm { P } ( B \mid A ) = \frac { 1 } { 6 }$. What is the value of $\mathrm { P } \left( A ^ { C } \mid B \right)$? (Here, $A ^ { C }$ is the complement of $A$.) [3 points]
(1) $\frac { 1 } { 2 }$
(2) $\frac { 7 } { 12 }$
(3) $\frac { 2 } { 3 }$
(4) $\frac { 3 } { 4 }$
(5) $\frac { 5 } { 6 }$

For two events $A$ and $B$, $\mathrm { P } ( A ) = \frac { 1 } { 2 } , \mathrm { P } \left( B ^ { C } \right) = \frac { 2 } { 3 }$, and $\mathrm { P } ( B \mid A ) = \frac { 1 } { 6 }$. What is the value of $\mathrm { P } \left( A ^ { C } \mid B \right)$? (Here, $A ^ { C }$ is the complement of $A$.) [3 points]\\
(1) $\frac { 1 } { 2 }$\\
(2) $\frac { 7 } { 12 }$\\
(3) $\frac { 2 } { 3 }$\\
(4) $\frac { 3 } { 4 }$\\
(5) $\frac { 5 } { 6 }$

Paper Questions

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