03cond - EECS 501 CONDITIONAL PROBABILITY Fall 2001 Three...

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Unformatted text preview: EECS 501 CONDITIONAL PROBABILITY Fall 2001 Three There are 3 cards: red/red; red/black; black/black. Card The cards are shuffled and one chosen at random. Monte The top of the card is red. Pr[bottom is red]=? 3 possible lines of reasoning to solve this problem: 1. Bottom is red only if chose red/red card Pr = 1 / 3. 2. Not black/black, so either red/black or red/red Pr = 1 / 2. 3. 5 hidden sides: 2 red and 3 black Pr = 2 / 5. Which is correct? They are ALL wrong! In fact, Pr = 2 / 3. DEF: Pr [ A | B ] = Pr [event A occurs, GIVEN THAT event B occurrED]. Either A occurs or A doesnt occur, even if B occurred. Their relative probabilities (ratio) shouldnt change, after restriction to B occurring ( A B and A B ). Want: Pr [ A | B ] + Pr [ A | B ] = 1 and Pr [ A | B ] Pr [ A | B ] = Pr [ A B ] Pr [ A B ] . Know: Pr [ A B ] + Pr [ A B ] = Pr [ B ]. So just divide this by Pr [ B ]. THM: Pr [ A | B ] = Pr [ A B ] /Pr [ B ] = Pr [ A B ] / ( Pr [ A B ] + Pr [ A B ])....
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This note was uploaded on 07/22/2011 for the course EECS 370 taught by Professor Lehman during the Spring '10 term at University of Florida.

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03cond - EECS 501 CONDITIONAL PROBABILITY Fall 2001 Three...

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