# hw1 - C Suppose you perform an experiment where there are...

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Math 310-1 (Fall 2011) Homework #1 Due date: Wednesday 9/28 in class A) Suppose you have two bags each containing three balls: one red, one blue, and one yellow. Suppose you draw one ball from each bag at random (drawing a total of two balls) such that each combination of balls is drawn equally likely. (a) Describe the probability space for this experiment. What is the size of the sample space? (b) Find the probability that the two balls are of the same color. (c) Find the probability that the two balls are of diﬀerent colors. (d) Find the probability that at least one of the two balls is red. B) Three horses A , B , and C are in a race. A is twice as likely to win as B , and B is twice as likely to win as C . (a) Find their respective probabilities of winning, that is, ﬁnd P ( A ), P ( B ), P ( C ). (b) Find the probability that B or C wins.
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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.

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