Unformatted text preview: will arrive at
the meeting place with a delay between 0 and 1 hour, with all pairs of
delays being equally likely. The ﬁrst to arrive will wait for 15 minutes
and will leave if the other has not yet shown up. What is the probably
that they will meet? M. Chen ([email protected]) ENGG2430C lecture 2 20 / 23 Birthday Paradox (Exercise) There are in total 83 students in our ENGG2430C class. Assuming
every student’s birthday is distributed among the 365 days uniformly
at random. (Hint: one way to compute P (A) is to compute P (Ac );
then P (A) = 1 − P (Ac ))
What is the probability that two selected students have the same
birthday? (Answer: 1/365)
What is the probability that among three selected students, at least
two of them have the same birthday?
What is the probability that among 83 students, at least two of them
have the same birthday? M. Chen ([email protected]) ENGG2430C lecture 2 21 / 23 Birthday Attack (Exercise) The mathematics behind the birthday paradox led to a wellknown
cryptographic attack called the birthday attack, which uses this
probabilistic model to reduce the complexity of cracking a hash
function.
Given a function f (x ) with N inputs and M distinct outputs (N is
much larger than M ), the goal of the attack is to ﬁnd two diﬀerent
inputs x1 , x2 such that f (x1 ) = f (x2 ). Such a pair x1 , x2 is called a
collision. (wiki)
Suppose we generate n inputs x1 , x2 , · · · , xn uniformly at random. How
large do we need to choose n, so that the probability of collision is at
least 0.5? M. Chen ([email protected]) ENGG2430C lecture 2 22 / 23 Thank You Reading: Ch. 1.1 1.2, and 1.3 of the textbook
Next lecture: Conditional probability and independence
Motivating scenarios:
A couple has two kids. Given that one of them is a boy, what is the
chance that the other one is also a boy?
A couple has two kids. Given that the elder one is a boy, what is the
chance that the other one is also a boy?
(Inside some Android input method) The ﬁrst two letters you type are
’y’ and ’o’. What is the likelihood that the third letter you will type is
an “u"? M. Chen ([email protected]) ENGG2430C lecture 2 23 / 23...
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This document was uploaded on 03/31/2014.
 Spring '14

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