Let E^Cdenote the complement of an event E. Let E_1 ,E_2and E_3be any pairwise independent events with P (E_1 )0and P (E_1 ∩E_2 ∩E_3 )=0Then P (E_2^C ∩E_3^C/E_1 ) is equal to:

Question

Let E^Cdenote the complement of an event E. Let E_1 ,E_2and E_3be any pairwise independent events with P (E_1 )>0and P (E_1 ∩E_2 ∩E_3 )=0Then P (E_2^C ∩E_3^C/E_1 ) is equal to:

Accepted Answer

Correct answer: D. (d)JEE Main 2020 Here P ( E_2^C ∩E_3^CE_1 )= P (E_1 ∩ (E_2^C ∩E_3^C ) )P (E_1 ) = P (E_1 )- [P (E_1 ∩E_2 )+P (E_2 ∩E_3 )-P (E_1 ∩E_2 ∩E_3 ) ]P (E_1 ) = P (E_1 )-P (E_1 ∩E_2 )-P (E_2 ∩E_3 )+0P (E_1 ) =1-P (E_2 )-P (E_3 ) =P (E_2^C )-P (E_3 ) or P (E_3^C )-P (E_2 )

$Let E^{C} denote the complement of an event E . Let E_{1}, E_{2} and E_{3} be any pairwise independent events with P (E_{1}) > 0 and P (E_{1} \cap E_{2} \cap E_{3}) = 0 Then P (E_{2}^{C} \cap E_{3}^{C} / E_{1}) is equal to:$

Solution

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