A) \[\frac{2}{9}\]
B) \[\frac{4}{9}\]
C) \[\frac{2}{3}\]
D) \[\frac{2}{7}\]
Correct Answer: B
Solution :
Let us consider the following events. |
\[\operatorname{A}:\]Card shows up black |
\[{{\operatorname{B}}_{1}}:\]Card with both sides black |
\[{{\operatorname{B}}_{2}}:\]Card with both sides white |
\[{{\operatorname{B}}_{3}}:\]Card with one side white and one black |
\[P({{B}_{1}})=\frac{2}{10},P({{B}_{2}})=\frac{3}{10},P({{B}_{3}})=\frac{5}{10}\] |
\[P\left( \frac{A}{{{B}_{1}}} \right)=1,P\left( \frac{A}{{{B}_{2}}} \right)=0,P\left( \frac{A}{{{B}_{3}}} \right)=\frac{1}{2}\] |
\[\operatorname{P}\left( \frac{{{B}_{1}}}{{{A}_{1}}} \right)=\frac{\frac{2}{10}\times 1}{\frac{2}{10}\times 1+\frac{3}{10}\times (0)+\frac{5}{10}\times \frac{1}{2}}\] |
\[=\frac{4}{4+5}=\frac{4}{9}\] |
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