JEE Mains · Maths · STD 12 - 13. probability
If \(A\) and \(B\) are any two events such that \(P\left( A \right)\, = \frac{2}{5}\) and \(P\left( {A \cap \,B} \right)\, = \frac{3}{{20}},\) then the conditional probability, \(P\left( {A\,|\,A'\, \cup \,B')} \right),\) where \(A'\) denotes the complement of \(A,\) is equal to
- A \(11/20\)
- B \(5/17\)
- C \(8/17\)
- D \(1/4\)
Answer & Solution
Correct Answer
(B) \(5/17\)
Step-by-step Solution
Detailed explanation
\(P(A)=\frac{2}{5}=\frac{8}{20} ; P(A \cap B)=\frac{3}{20}\) \(P(\overline{A \cap B})=1-\frac{3}{20}\) \(\Rightarrow \quad P(\bar{A} \cup \bar{B})=\frac{17}{20}\) \({A \cap\left(A^{\prime} \cup B^{\prime}\right)} \) \({=A-(A \cap B)} \) \(\therefore \)…
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