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For the following questions, choose the correct answer from the codes (a),(b),(c ) and (d) defined as follows. Let `H_(1),H_(2),.........H_(n)` be mut

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For the following questions, choose the correct answer from the codes (a),(b),(c ) and (d) defined as follows. Let H_(1),H_(2),.........H_(n) be mutually exclusive events with P(H_(i)) gt 0,i=1,2,.......n,.Let E be any other event with 0 lt P(E ) lt 1. Statement I P(H_(i)|E ) gt 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 Select the correct answer from above options

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Correct Answer - D Statement I if P(Hi∩E)=0 for some I, then P( Hi E )=P( E Hi )=0 If P(Hi∩E)≠O,∀ i=1,2,...,n,then P( Hi E )= P(Hi∩E) P(Hi) × P(Hi) P(E) = P( E Hi )×P(Hi) P(E) >P( E Hi )⋅P(Hi) [∴O<P(E)<1] Hence, Statement I may not always be true. Statement II Clearly, H1∪H2∪...∪Hn=S [same space ] ⇒ P(H1)+P(H2)+...+P(Hn)=1 Hence, Statement II is true.

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