JEE Mains · Maths · STD 12 - 13. probability
Let \(A\) and \(B\) be two events such that \(P ( B \mid A )=\frac{2}{5}\), \(P ( A \mid B )=\frac{1}{7}\) and \(P ( A \cap B )=\frac{1}{9} .\) Consider \(( S 1) P \left( A ^{\prime} \cup B \right)=\frac{5}{6}\) \(( S 2) P \left( A ^{\prime} \cap B ^{\prime}\right)=\frac{1}{18}\). Then.
- A Both \(( S 1)\) and \(( S 2)\) are true
- B Both \(( S 1)\) and \(( S 2)\) are false
- C Only \((S1)\) is true
- D Only \((S2)\) is true
Answer & Solution
Correct Answer
(A) Both \(( S 1)\) and \(( S 2)\) are true
Step-by-step Solution
Detailed explanation
\(P ( A \mid B )=\frac{1}{7} \Rightarrow \frac{ P ( A \cap B )}{ P ( B )}=\frac{1}{7}\) \(P(B)=\frac{7}{9}\) \(P(B \mid A)=\frac{2}{5} \Rightarrow \frac{P(A \cap B)}{P(A)}=\frac{2}{5}\) \(P ( A )=\frac{5}{18}\) Now, \(P\left(A^{\prime} \cup B\right)=1-P(A \cup B)+P(B)\)…
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