What is the probably that they will meet m chen

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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 (IE@CUHK) 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 (IE@CUHK) ENGG2430C lecture 2 21 / 23 Birthday Attack (Exercise) The mathematics behind the birthday paradox led to a well-known 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 (IE@CUHK) 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 (IE@CUHK) ENGG2430C lecture 2 23 / 23...
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