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For two events E(1) and E(2), P(E(1))=1/...

For two events `E_(1)` and `E_(2), P(E_(1))=1/2,P(E_(2))=1/3` and `P(E_(1)nnE_(2))=1/10`. Find:
(i) `P(E_(1) "or" E_(2))`
(ii) `P(E_(1) "but not" E_(2))`
(iii) `P(E_(2)"but not" E_(1))`
(iv) `P` (neithter `E_(1)` not `E_(2)`)

Text Solution

Verified by Experts

The correct Answer is:
N/a
`P(barE_(1))=1-P(E_(1))=1-1/2=1/2`
`P(barE_(2))=1-P(E_(2))=1-1/3=2/3`
(i) `P(E_(1)"or"E_(2))=P(E_(1)uuE_(2))`
`=P(E_(1))+P(E_(2))-P(E_(1)nnE_(2))`
`=1/2+1/3-1/10`
`=(15+10-3)/30=11/15`
(ii) `P(E_(1) "but not" E_(2))=P(E_(1)nnbarE_(2))`
`=P(E_(1))-(E_(1)nnE_(2))`
`=1/2-1/10`
`=(5-1)/10=2/5`
(iii) `P(E_(2)"but not"E_(1))=P(E_(2)nnbarE_(1)))`
`=P(E_(2))-P(E_(2)nnE_(1))`
`=1/3-1/10=(10-3)/30=7/30`
(iv) `P` (neither `E_(1)` nor `E_(2))=P(barE_(1)nnbarE_(2))`
`=Pbar((E_(1)uuE_(2)))`
`=1-P(E_(1)uuE_(2))`
`1-11/15=4/15`
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