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Intersection and union to explore the probability function

Q: Let A and B be two events defined on a sample space S such that

P(A or B)=0.7 [P(A union B)=0.7]

Find the following

(1) P(A and B) [P(A intersect B)]
(2) P(A^C and B) [P(A complement intersect B)]

See word document for a cleaner version of the problem.


Solution Preview

(1) When events are mutually exclusive a very helpful formula is P(A union B)=P(A)+P(B).

However, in our example, events A and B are clearly not mutually exclusive (prove this for yourself). So, the proper formula would become P(A union B)=P(A)+P(B)-P(A intersect ...

Solution Summary

We use the the concepts of "intersection" and "union" to explore the probability function. We learn about an event and its complement, and how to find the probability of the intersection of events mathematically. A few simple examples illustrate these ideas.