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# lecture1.pdf - COMPSCI 240 Reasoning Under Uncertainty Arya...

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COMPSCI 240: Reasoning Under Uncertainty Arya Mazumdar University of Massachusetts at Amherst Fall 2016

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Lecture 1
Where do we start? Antoine Gombaud, Chevalier de M´ er´ e Wikipedia: M´ er´ e was an important Salon theorist. Like many 17th century liberal thinkers, he distrusted both hereditary power and democracy. He believed that questions are best resolved in open discussions among witty, fashionable, intelligent people. He was also a gambler (or was he?).

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Chevalier de M´ er´ e Problem: a version of a story Figure: A die (or dice) A game of dice-throwing: Two dice. 24 throws. Both show Ace. de M´ er´ e lost money - he kept loosing money.
The de M´ er´ e argument There is 1 / 6 chance that an Ace will turn up. By throwing a die 4 times there is more than 50% chance that there will be an Ace For the second die an Ace will turn up on average in 6 throws So 4 × 6 = 24 throws must give more than 50% chance of winning But he still lost more than he won

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Gamblers may have Mathematician friends (or they can hire mathematicians) Blaise Pascal (1623-1662; A programming language; also a unit of pressure) Pierre de Fermat (1607-1665; Also known for a last theorem) What did they decide? We will know soon enough.
Why do we need reasoning under uncertainty? To gamble!! But also for Planning and Routing: You study all night and wake up 15 minutes before your exam. You could take a 10 minute bus ride but you have to catch a bus first: each minute, a bus to school passes your house with probability 1/5. Your other choice is to bike to the University from home, but it will take you 20 minutes. Should you wait for the bus or hop on your bike? (Thanks Andrew McGregor for this example)

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Why do we need reasoning under uncertainty?
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• Fall '12
• Ben
• Set Theory, Probability theory, probability density function

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