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Let H1, H2, , Hn be mutually exclusive ...

Let `H_1, H_2, , H_n` be mutually exclusive and exhaustive events with `P(H_i)>0,i=1,2,...,n.` Let `E` be any other event with `0 < P(E) < 1.` Statement 1: `P(H_i|E) > P(E|H_i .P(H_i) for i=1,2,.......,n` statement II `sum_(i=1)^n P(H_i)=1`

A

Statement I is true, Statement II is also true, Statement II is the the correct explanation of Statement I

B

Statement I is true, Statement II is also true, Statement II is is not the correct explanation of Statement I

C

Statement I is true,Statement II is false

D

Statement I is false, Statement II is true

Text Solution

Verified by Experts

The correct Answer is:
D
Statement I if `P(H_(i)nnE)=0` for some I, then
`P((H_(i))/(E))=P((E)/(H_(i)))=0`
If `P(H_(i)nnE)neO,AA " " i=1,2,...,n,`then
`P((H_(i))/(E))=(P(H_(i)nnE))/(P(H_(i)))xx(P(Hi))/(P(E))`
`=(P((E)/(H_(i)))xxP(H_(i)))/(P(E))gtP((E)/(H_(i)))*P(H_(i))" " [therefore OltP(E)lt1]`
Hence, Statement I may not always be true.
Statement II Clearly, `H_(1)uuH_(2)uu...uuH_(n)=S`
[same space ]
`rArr " " P(H_(1))+P(H_(2))+...+P(H_(n))=1`
Hence, Statement II is true.
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