# Two Proofs in Probability Theory

Let (S, E, P) be a probability space.

(a) Let A <- E be an event such that P(A) = 0. Does it follow that A = PHI? If not, what can you say about A?

(b) Prove that if A, B <- E, then A INTERSECTION B <- E and A - B <- E.

https://brainmass.com/math/probability/two-proofs-probability-theory-426482

#### Solution Preview

(a) P(A) = 0 does not imply that A is empty - it just means that A has an infinitesimal probability of occurring. For example, consider the probability space of points on the line segment S = [0,1] with uniform probability distribution, i.e. if L is a subsegment of S, then P(L) is ...

#### Solution Summary

This solution of 258 words proves two statements in probability theory.

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