Lecture 9 - sept 30

# Whats the probability that a person who likes kanye

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- what’s the probability that a person who likes Kanye West also likes Katie Perie? - 50 people like both KP and KW - 150 people like katie not kanye - 150 like kanye not katie - if you know they like KW can you predict if they will like KP? - P (KP|KW) (| means “given”); mathematical question - how do you answer this? - build a contingency table - 4 states: like both, like one, like other, like none KP + - + 50 150 200 KW - 150 ? - we need to know how many people in “marginals” - add 2 numbers.. ONLY NEED top half of table - only care with that line - so to know if they will like KP: 50 who like KW also like katie but its out of 200 - therefore P = 50/200 = 0.25 - P (KW|KP) = left hand column also is 50/200 = 0.25 Sept. 30th, 2010

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- P (that we like KW that we don’t like KP) - need more info -P ( I & B) = 495/500 = 99% - need to know the neither in order to fill out the table - if it was 10 00 and not 500 - then the whole percent changes - it seems counter intuitive that to answer the question of what proportion like both that we need to know how many like neither -because in order to have the base rate we need all values - if the 0 was 10 000 then the 500 is then 10 500 and then its 4.7 % not 99% - people have a very hard time learning this HIV TESTING (making numbers up): - base rate: 1% of ppl tested actually have it - if 10 000 ppl tested, how many ppl have it? 100. - that doesn’t mean 100 people will show it in the test, tests are not perfect - this is why the contingency test helps - suppose friend goes in for HIV test and tests positive, 98% accurate. What is the likelihood that your friend ACTUALLY has the disease? - test can be positive or negative - person can be positive or negative - sometimes the test says you have the disease when you don’t - and sometimes the test says you don’t when you do - wrong 2% of the time. - 10 000 people tested, 100 people have it - 98 people test positive and have it, while 2 test negative and have it - if 100 have it, how many don’t? 9900 - 2 % of time person does NOT have it, test will say it does - 198: 98% test is accurate, .98 x 9900 = 9702/198 - 296 people have a positive test out of 10 000 and only 98 of those people actually have it - you can test positive 98/296 = 33% and have less than 50% chance of having the disease 2 Poison Problem - go to eat at a restaurant and wake up feeling terrible, face all blue - doctor tells you there are 2 food poisoning, one turns face blue and one turns face green - pill will cure you but if you take the wrong pill you will die - 10% of doctors could do this right and the other 90% would have killed their patient - green disease = 5x more common - colour of face consistent with disease 75% of the time - 1000 people have green disease, therefore 200 people have blue (5x less) - face green 75% of 1000 = 750, leaving 250 Sept. 30th, 2010
- face blue 75% of 200 = 150 leaving 50 with green face - if you have blue face what should you do? - Probability of blue face with blue pill curing, 150/400 = 37% - if your face was green then you would take the green pill for sure! - Sept. 30th, 2010
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• Winter '10
• Fountain,M
• Psychology, Want, nucleus accumbens, Mesolimbic pathway, The Other Person

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