A) \[\frac{89}{180}\]
B) \[\frac{90}{180}\]
C) \[\frac{91}{180}\]
D) \[\frac{92}{180}\]
Correct Answer: A
Solution :
\[\because \]\[P(A)=\frac{1}{12},P(B)=\frac{5}{12}\]and \[P\left( \frac{B}{A} \right)=\frac{1}{15}\] We know that \[P\left( \frac{B}{A} \right)=\frac{P(A\cap B)}{P(A)}\] \[\Rightarrow \] \[\frac{1}{15}=\frac{P(A\cap B)}{\frac{1}{12}}\] \[\Rightarrow \] \[P(A\cap B)=\frac{1}{180}\] Also, \[P(A\cup B)=P(A)+P(B)-P(A\cap B)\] \[=\frac{1}{12}+\frac{5}{12}-\frac{1}{180}\] \[=\frac{15+75-1}{180}=\frac{89}{180}\]
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