Classof41410

# Classof41410 - COMPUTING PROBABILITIES and CONDITIONAL...

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COMPUTING CONDITIONAL PROBABILITIES PROBABILITIES and

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Arrangements, Colorings n k next next 3) Probability no two equal colors n ( n - 1)( n - 2) ··· ( n - k +1) n k = (1 - 1 n )(1 - 2 n )(1 - 3 n ) · · · (1 - k - 1 n )
The birthday problem What is the probability that in a class with k students at least two have the same birthday? next How large a class must be so that the probability that at least two students will have the same birthday is more than 50% ????? 1 - (1 - 1 n )(1 - 2 n )(1 - 3 n ) · · · (1 - k - 1 n ) n = 365

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Monty Hall Marylin vos Savant Behind one door is a car behind the others goats. He then says to you: “do you want to pick door 2 ?” Is it to your advantage to take the switch? The question The Monty Hall Paradox Suppose you are in a game show and you are given the choice of three doors: You pick a door, say No 1. The host, who knows what is behind the doors opens another door, say No 3 which has a goat. next
Don’t guess Draw the wheel The innermost wheel gives the door that has the car The middle wheel gives the door you choose The outermost wheel gives the door that is opened by the host next

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If the host opens the door that has the car spin again! No need to switch
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## This note was uploaded on 09/22/2010 for the course MATH MATH187 taught by Professor Math187 during the Spring '10 term at UCSD.

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Classof41410 - COMPUTING PROBABILITIES and CONDITIONAL...

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