If E1-E2 are two events with E1- E2- then PE1-E2-

We know, P(E_1∩E_2)=1 P(E_1∪ E_2) =1 [P(E_1)+P(E_2)] (∵ P(E_1∩ E_2)=ϕ) =[1 P(E_1)] P(E_2) =P(E_1) P(E_2) nbsp; or nbsp; P(E_2) P(E_1) nbsp; ...

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Byju's Answer

Standard XI

Mathematics

Complement of a Set

If E1,E2 are ...

Question

If $E_{1}, E_{2}$ are two events with $E_{1} \cap E_{2} = ϕ,$ then $P ({¯ ¯¯ ¯ E}_{1} \cap {¯ ¯¯ ¯ E}_{2}) =$

P ({¯ ¯¯ ¯ E}_{1}) - P (E_{2})

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P ({¯ ¯¯ ¯ E}_{2}) - P (E_{1})

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P (E_{2}) - P (E_{1})

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P ({¯ ¯¯ ¯ E}_{2}) - P ({¯ ¯¯ ¯ E}_{1})

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Solution

The correct option is B $P ({¯ ¯¯ ¯ E}_{2}) - P (E_{1})$
We know,
$P ({¯ ¯¯ ¯ E}_{1} \cap {¯ ¯¯ ¯ E}_{2}) = 1 - P (E_{1} \cup E_{2}) = 1 - [P (E_{1}) + P (E_{2})] (∵ P (E_{1} \cap E_{2}) = ϕ) = [1 - P (E_{1})] - P (E_{2}) = P ({¯ ¯¯ ¯ E}_{1}) - P (E_{2}) or P ({¯ ¯¯ ¯ E}_{2}) - P (E_{1})$

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Complement of a Set

Standard XI Mathematics

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