JEE Mains · Maths · STD 12 - 13. probability
Let \(E ^{ C }\) denote the complement of an event \(E\). Let \(E _{1}, E _{2}\) and \(E _{3}\) be any pairwise independent events with \(P \left( E _{1}\right) > 0\) and \(P \left( E _{1} \cap E _{2} \cap E _{3}\right)=0\) Then \(P \left( E _{2}^{ C } \cap E _{3}^{ C } / E _{1}\right)\) is equal to
- A \(\mathrm{P}\left(\mathrm{E}_{3}^{\mathrm{C}}\right)-\mathrm{P}\left(\mathrm{E}_{2}\right)\)
- B \(\mathrm{P}\left(\mathrm{E}_{2}^{\mathrm{C}}\right)+\mathrm{P}\left(\mathrm{E}_{3}\right)\)
- C \(\mathrm{P}\left(\mathrm{E}_{3}^{\mathrm{C}}\right)-\mathrm{P}\left(\mathrm{E}_{2}^{\mathrm{C}}\right)\)
- D \(\mathrm{P}\left(\mathrm{E}_{3}\right)-\mathrm{P}\left(\mathrm{E}_{2}^{\mathrm{C}}\right)\)
Answer & Solution
Correct Answer
(A) \(\mathrm{P}\left(\mathrm{E}_{3}^{\mathrm{C}}\right)-\mathrm{P}\left(\mathrm{E}_{2}\right)\)
Step-by-step Solution
Detailed explanation
Given \(\mathrm{E}_{1}, \mathrm{E}_{2}, \mathrm{E}_{3}\) are pairwise indepedent events \(\operatorname{soP}\left(\mathrm{E}_{1} \cap \mathrm{E}_{2}\right)=\mathrm{P}\left(\mathrm{E}_{1}\right) \cdot \mathrm{P}\left(\mathrm{E}_{2}\right)\) and…
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