Unformatted text preview: C) Suppose you perform an experiment where there are eight possible outcomes. If every subset of outcomes constitutes an event, how many distinct events are there? D) A point X is selected at random (with uniform probability) from a line segment AB with midpoint O . Find the probability p that the line segments AX , XB , and AO can form a triangle. ( Hint: In a triangle, the sum of the lengths of any two sides must be at least the length of the third side.) E) Let (Ω , A ,P ) be a probability space. (a) Prove (using the deﬁnition of probability space) that if E and F are events with E ⊆ F , then P ( E ) ≤ P ( F ). (b) Prove that given any two events E and F , P ( E T F ) ≥ P ( E ) + P ( F )-1. From the textbook: pp 22 # 1 - 4, and # 6 - 11....
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This note was uploaded on 10/03/2011 for the course MATH 310-1 taught by Professor Sarver during the Spring '11 term at Northwestern.
- Spring '11