यदि `E_(1),E_(2)` दो घटनाऐं है `P(E_(1))=0.5,P(E_(2))=0.3" तथा "P(E_(1)" तथा "E_(2))=0.1` तो ज्ञात कीजिए-
(i) `P(E_(1)" या "E_(2))` (ii) `P(E_(1)" परन्तु "E_(2)" नहीं ")`
(iii) `P(E_(2)" परन्तु "E_(1)" नहीं ")`
(iv) `P("न "E_(1)" न "E_(2))`

Explanation

`P(E_(1))=0.5,P(E_(2))=0.3,P(E_(1)nnE_(2))=0.1`
`impliesP(bar(E)_(1))=1-0.5=0.5" तथा "P(bar(E)_(2))=1-0.3=0.7`
तब (i) `P(E_(1)" या "E_(2))=P(E_(1)uuE_(2))=P(E_(1))+P(E_(2))-P(E_(1)nnE_(2))=0.5+0.3-0.1=0.7`
(ii) `P(E_(1)" परन्तु "E_(2)" नहीं ")=P(E_(1)nnbar(E)_(2))=P(E_(1))-P(E_(1)nnE_(2))=0.5-0.1=0.4`
(iii) `P(E_(2)" परन्तु "E_(1)" नहीं ")=P(E_(2)nnbar(E)_(1))=P(E_(2))-P(E_(2)nnE_(1))=0.3-0.1=0.2`
(iv) `P(" न "E_(1)" न "E_(2))=P((bar(E)_(1)nnbar(E)_(2)))/(P=(E_(1)uuE_(2)))=1-P(E_(1)uuE_(2))`
`=1-P(E_(1)" या "E_(2))=1-0.7=0.3`