HW#4, Due 03/18
AMS 311 Probability Theory (Spring 2011)
Read: Ross, Chapter 4, Sections 4.5–4.9.
(you can skip the Hypergeometric distribution
(4.8.3) and the Zeta distribution (4.8.4)), Sections 5.1–5.3.
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). (10 points) Suppose it takes at least 9 votes from a 12member jury to convict a defendant.
Suppose the probability that a juror votes a guilty person innocent is 0.2, whereas the probability
that the juror votes an innocent person guilty is 0.1. If each juror acts independently and if 65
percent of the defendants are guilty, find the probability that the jury renders a correct decision.
(you need not evaluate any arithmetic expression)
*** Please denote the events with letters clearly. (e.g., Let C be the event that the defendant is
convicted (found to be guilty by at least 9 of the 12 jurors). Let G be the event that the defendant
actually is guilty. Let E be the event that the jury renders a correct decision. The problem asks
you to compute P(E).)
(2). (10 points) A certain typing agency employs Alan, Bob, and Cathy as typists. The average
number of errors per page is 3 when typed by Alan, 4.2 when typed by Bob, and 2.1 when typed
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 Spring '08
 Tucker,A

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