lec0330 - CS 173 Discrete Mathematical Structures Cinda...

CS 173:
Discrete Mathematical Structures
Cinda Heeren
[email protected]
Siebel Center, rm 2213
Office Hours: BY APPOINTMENT

Cs173 - Spring 2004
CS 173
Announcements
Homework 9 available. Due 04/ 02, 8a.
Exam 2, Apr 4, 7-9p, Loomis 141. Email Cinda
with conflicts.
Today’s lecture covers material from Rosen,
sections 5.2-5.3.

Cs173 - Spring 2004
CS 173
Birthdays
How many people have to be in a room to assure
that the probability that at least two of them have
the same birthday is greater than 1/ 2?
a) 23
b) 183
c) 365
d) 730
Let p
n
be the probability that no people share a birthday
among n people in a room.
We want the smallest n so that 1 - p
n
> 1/ 2.
Then 1 - p
n
is the probability that 2 or more share a birthday.

Cs173 - Spring 2004
CS 173
A Special Random Variable
A Binomial random variable X is a random variable
that counts the number of successes in a sequence
of n independent Bernoulli trials, where the
probability of success on each trial is p.
What are the possible values for X?
1, 2, …n
We want Pr(X = k), k = 1,…n.
From last time,
Pr(X = k) = C(n, k) p
k
(1-p)
n-k

Cs173 - Spring 2004
CS 173
A Special Random Variable
Suppose a network consisting of 10 computers
crashes completely if there are not at least 8
functioning machines. Further, suppose that each
machine functions with probability 0.9,
independently of the others.
What is the probability the network is available?