MIT6_042JS10_lec34_sol

# MIT6_042JS10_lec34_sol - Massachusetts Institute of...

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Unformatted text preview: Massachusetts Institute of Technology 6.042J/18.062J, Spring ’10 : Mathematics for Computer Science Prof. Albert R. Meyer revised April 26, 2010, 1303 minutes Solutions to In-Class Problems Week 12, Fri. Problem 1. There are two decks of cards. One is complete, but the other is missing the ace of spades. Sup- pose you pick one of the two decks with equal probability and then select a card from that deck uniformly at random. What is the probability that you picked the complete deck, given that you selected the eight of hearts? Use the four-step method and a tree diagram. Solution. Let C be the event that you pick the complete deck, and let H be the event that you select the eight of hearts. In these terms, our aim is to compute: Pr { C ∩ H } Pr { C | H } = Pr { H } A tree diagram is worked out below: card selected 8 hearts other 2 1/52 51/52 complete? 8 of hearts? probability X X X 1/104 51/104 Now we can compute the desired conditional probability as follows: Creative Commons 2010, Prof. Albert R. Meyer . 2 Solutions to In-Class Problems Week 12, Fri. Pr { C H } = Pr { C ∩ H } | Pr { H } 1 1 = 2 52 · 1 1 + 1 1 2 52 2 51 · · 51 = 103 = 0 . 495146 ... Thus, if you selected the eight of hearts, then the deck you picked is less likely to be the complete one. It’s worth thinking about how you might have arrived at this final conclusion without going through the detailed calculation. through the detailed calculation....
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## This note was uploaded on 05/27/2011 for the course CS 6.042J taught by Professor Prof.albertr.meyer during the Spring '11 term at MIT.

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MIT6_042JS10_lec34_sol - Massachusetts Institute of...

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