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By rolling a die the following events ar...

By rolling a die the following events are considered `E_(1)={5,3,1},E_(2)={3,2},E_(3)={5,4,3,2}`. The arrangement of the following probabilities `A:P((E_(1))/(E_(2))), quad B:P(E_(1)uu E_(3)), C:P(E_(1)nnE_(3)), D:P(E_(2)nn E_(1))` in ascending order is

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By rolling a die the following events are considered E_(1)={5,3,1},E_(2)={3,2},E_(3)={5,4,3,2} . The arrangement of the following probabilities A:P((E_(1))/(E_(2))),quad B:P(E_(1)uu E_(3)), C:P(E_(1)nn E_(3)), D:P(E_(2)nn E_(1)) In descending order is

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If E_(1) and E_(2) be two events such that P(E_(1))=0.3, P(E_(2))=0.2 and P(E_(1)nnE_(2))=0.1, then find: (i) P(barE_(1)nnE_(2)) (ii) P(E_(1)nnbarE_(2))

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If E_(1) nad E_(2) are two independent events such that P(E_(1))=0.3 and P(E_(2))=0.6 then find the value of (i)P(E_(1)nn E_(2)) (ii) P(E_(1)uu E_(2)) (iii) P((E_(1))/(E_(2)))( iv )P((E_(2))/(E_(1)))

If E_(1) and E_(2) are the two events such that P(E_(1))=1/4, P(E_(2))=1/3 and P(E_(1) uu E_(2))=1/2 , show that E_(1) and E_(2) are independent events.

If E_(1), E_(2), E_(3) are independent events, such that P(E_(1)nnbar(E_(2))nnbar(E_(3)))=1/4, P(bar(E_(1))nnbar(E_(2))nnbar(E_(3)))=1/8, P(bar(E_(1))nnE_(2)nnbar(E_(3)))=1/8 . Find P(bar(E_(3)))

Let E^(C) denote the complement of an event E. Let E_(1),E_(2) and E_(3) be any pairwise independent events with P(E_(1))gt0 and P(E_(1)nn E_(2) nn E_(3))=0 . Then P(E_(2)^(C)nnE_(3)^(C)//E_(1)) is equal to :

If E_(1) and E_(2) are events of a sample space such that P(E_(1))=(1)/(4),P((E_(2))/(E_(1)))=(1)/(2),P((E_(1))/(E_(2)))=(1)/(4) Then P((E_(1))/(E_(2)))=