An observed event B can occur after one of the three events `A_(1), A_(2), A_(3)`. If
`P(A_(1)) = P(A_(2)) = 0.4, P(A_(3)) = 0.2 and P(B//A_(1)) = 0.25, P(B//A_(2)) = 0.4, P(B//A_(3)) = 0.125`, what is the probability of `A_(1)` after observing B ?

For the A.P., a_(1),a_(2),a_(3) ,…………… if (a_(4))/(a_(7))=2/3 , find (a_(6))/(a_(8))

Let a_(1), a_(2), a_(3) , …..be in A.P. If (a_(1) + a_(2) + …. + a_(10))/(a_(1) + a_(2) + …. + a_(p)) = (100)/(p^(2)), p ne 10 , then (a_(11))/(a_(10)) is equal to :

If a_(1), a_(2),…a_(n) are in H.P. then a_(1).a_(2) + a_(2).a_(3) + a_(3).a_(4) + …+ a_(n-1) .a_(n) =

A_(1), A_(2) and A_(3) are three events. Show that the simultaneous occurrence of the events is P(A_(1) cap A_(2) cap A_(3))=P(A_(1))P(A_(2)//A_(1))P[A_(3)//(A_(1) cap A_(2))] State under which condition P(A_(1) cap A_(2) cap A_(3))=P(A_(1))P(A_(2))P(A_(3))

A_(1),A_(2) and A_(3) are three events.Show that the simultaneous occurrence of the events is P(A_(1)nn A_(2)nn A_(3))=P(A_(1))P((A_(2))/(A_(1)))P[((A_(3))/(A_(1)nn A_(2))] State under which condition P(A_(1)nn A_(2)nn A_(3))=(P(A_(1))P(A_(2))P(A_(3))

Let a_(1), a_(2), a_(3), ……… be terms of an A.P. if (a_(1) + a_(2) + ...... a_(p))/(a_(1) + a_(2) + ...... a_(q)) = p^(2)/q^(2) , p != q , then a_(6)/a_(21) equals

If A_(1);A_(2);....A_(n) are independent events associated with a random experiment; then P(A_(1)nA_(2)n......n_(n))=P(A_(1))P(A_(2))......P(A_(n))

if a,A_(1),A_(2),A_(3)......,A_(2n),b are in A.P.then sum_(i=1)^(2n)A_(i)=(a+b)