- #1

mrkb80

- 41

- 0

The question says:

Let

*P*be a probability function. Prove that for any finite collection of sets, the sequence A

_{1},A

_{2},...,A

_{n}of pairwise disjoint sets, P(Union from i=1 to n of A

_{i})=Ʃ from i=1 to n of A

_{i}

I think there must a mistake in question. My guess is it is supposed to say P(Union from i=1 to n of A

_{i})=Ʃ from i=1 to n of

**P(A**?

_{i})There is a hint with the question:

If A

_{1},A

_{2},...,A

_{n}are pairwise disjoints on the sample space Ω, then P(Union from i=1 to ∞ A

_{i}) = Ʃ from i=1 to ∞ A

_{i}

If A and B are disjoints defined on Ω then P(A U B) = P(A)+ P(B)

Again, I think there must be a mistake in the hint...P(Union from i=1 to ∞ A

_{i}) = Ʃ from i=1 to ∞

**P(A**?

_{i})My question is are there mistakes and can someone get me started in the right direction (Assuming the question has a mistake, then the book says the proof is a straight forward induction argument with P(A U B) = P(A) + P(B), if A and B are mutually exclusive events over S being the starting point)