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Unformatted text preview: what is the
probability that he/she has the disease?
Let A ={The person has the disease}, and B ={the test result is
positive}.
P (AB ) = P (B A) P (A)
0.001
= 0.95
= 0.0187.
P (B )
0.001 · 0.95 + 0.999 · 0.05 (80% of the questioned persons in US leading hospital answered the
probability that the person has the decease is 0.95!)
M. Chen (IE@CUHK) ENGG2430C lecture 4 10 / 19 Counting Based on Discrete Uniform Law Throw two dies. Event A ={sum of two dies gives 7}; P (A) =? Since all outcomes are equally likely, thus
P (A) =
M. Chen (IE@CUHK) number of outcomes in A
total number of outcomes in Ω
ENGG2430C lecture 4 11 / 19 Counting Principle r steps
ni choices at step i
Total umber of choices is: n1 n2 · · · nr (D. P. Bertsekas & J. N. Tsitsiklis, Introduction to Probability, Athena Scientiﬁc Publishers, 2002)
M. Chen (IE@CUHK) ENGG2430C lecture 4 12 / 19 Permutation: Order of Selection Matters The total number of ways to order n elements = n!
128 bits long IPv6 (Internet Protocol version 6) addresses will be used
to identify endhosts on the Internet. How many are they?
2128 ≈ 3.4 × 1038 . Number of subsets of {1, 2, . . . , n} = 2n
“Mark Six" lottery: six Drawn Numbers and one Extra Number, all
between 1 and 49.
Number of outcomes in Ω :
Event A ={all numbers of a outcome are even}
Number of outcomes in A:
P (A) =? M. Chen (IE@CUHK) ENGG2430C lecture 4 13 / 19 Combination: Order of Selection Does Not Matter k
Number of k element subsets of an nelement set: Cn =
(notations: http://en.wikipedia.org/wiki/Combination) n
k n
Question: ∑n =0 k =? Answer: 2n . Hint: how to relate it to the total
k
number of subsets of an nelement set? k
How to obtain the closedform expression of Cn ? Consider the following two ways of constructing an ordered sequence of
k distinct items
Choose the k items, one at a time:
n(n − 1) · · · (n − k + 1) = n!
(n − k )! Choose k items at one shot, then order them
k
Cn · k ! Thus
k
Cn =
M. Chen (IE@CUHK) n!
(n − k )!k ! ENGG2430C lecture 4 14 / 19 Partition 52...
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This document was uploaded on 03/31/2014.
 Spring '14

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