by induction show that pa1SolutionBy the process of inductio

by induction, show that p(a1

By the process of induction:

P(a1.a2) = P(a2|a1) * P(a1)

Let us assume:

P(a1.a2....ak) = P(ak | a(k-1)...a2.a1) * P(a(k-1) | a(k-2)...a2.a1)...P(a2 |a1).P(a1)

P(a1.a2.....ak.a(k+1)) = P(a(k+1) | P(ak.a(k-1)...a2.a1) * P(ak.a(k-1)...a2.a1)

[As P(A and B) = P(B|A)*P(A)]

= P(a(k+1) | P(ak.a(k-1)...a2.a1) * P(ak | a(k-1)...a2.a1) * P(a(k-1) | a(k-2)...a2.a1)...P(a2 |a1).P(a1)

[From our assumption]

Hence proved