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October 28, 2010
Math 351  Test 2
1. Suppose urn I has one red and three blue balls; suppose urn II has one red and ﬁve blue balls.
Pick one ball from each urn. You get $2 for each red one and $1 for each blue one. Let
X
be
the total number of dollars you win.
(a) Find the probability mass function of
X
.
(b) Find the variance of
X
.
2. Suppose urn I and urn II are as in the previous question; suppose urn III has one red and
one blue ball. Toss a sixsided die. If the die comes up 1 or 2 pick a ball from urn I; if the
die comes up 3,4 or 5 pick a ball from urn II; if the die comes up 6 pick a ball from urn III.
Calculate each of the following probabilities.
(a) The probability of the event that the ball is red.
(b) The probability of the event that the ball is red and it came from urn II.
(c) Say we see that the ball is red. What is the probability that it came from urn II?
(d) Are the events “ball is red” and “ball came from urn I” independent? Credit only for a
mathematical reason.
(e) Are the events “ball is red” and “ball came from urn II” independent? Credit only for
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This note was uploaded on 03/05/2011 for the course MATH 351 taught by Professor Moumen,f during the Spring '08 term at George Mason.
 Spring '08
 Moumen,F
 Math, Probability

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