HW#1, Due 02/16
AMS 311 Probability Theory (Spring 2011)
Read: Ross, sections 1.11.4 of Ch1, and section 2.12.5 of Ch2. You’d better go through the following
examples before doing the assignments: Ch1: 2a2e; 3a3f; 4a4e; Ch2: 3a, 3b, 4a, 5a5j, 5l
Part 1 (10 points):
PRINT
your name and StonyBrook ID (
Last, First, #ID
) on the top on your work
sheet. Staple your HW if more than 1 pages.
Part 2: Problems (90 points)
Write down your work step by step to get full score.
(1). (8 points)
Let A and B be two events in sample space
S
. If P(A)=.9, and P(B)=.8, show that P(A∩B) ≥0.7.
In general, prove Bonferroni’s inequality, namely, P(A∩B) ≥ P(A) + P(B) − 1.
(2). (15 points)
There are 6 people at the security check at JFK, each with a laptop. Unfortunately, all the laptops
look identical. They put them through the machine and each person grabs a laptop at random on
the other side, not noticing that they may not have grabbed their own.
(a). Describe the sample space corresponding to this experiment. (Make certain to define the
notation you use to specify the outcomes!)
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 Spring '08
 Tucker,A
 Probability, Probability theory, possible value, lowest homework grade

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