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# Of those who do not have the disease 90 test negative

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Unformatted text preview: ot have the disease, 90% test negative when the test is applied. Suppose that an individual from this population is randomly selected and given the screening test. Define NUS/FoS/DSAP A = having the disease B = tested positive 7 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with Probabilities (Continued) Problem 4... Medical Screening √ False Positive: Gotten a positive test result of disease when the person is healthy w/o disease P(B | A ) = √ False Negative: Gotten a negative test result of disease when the person has the disease P ( B | A) = √ Our goal is too keep both false positive and false negative rates low... However, these two rates work against each other. NUS/FoS/DSAP 8 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with Probabilities (Continued) Problem 4... Medical Screening √ In medical screening, it is first and foremost desirable to have a low false negative rate to catch as many affected disease cases as possible A high sensitivity of a screening test usually means a _______ false negative rate. That is, very few cases go undetected. √ A low specificity of a screening test usually means a _______ false positive rate. That is, very many cases are identified with the disease symptoms, but not having the disease. NUS/FoS/DSAP 9 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with Probabilities (Continued) Problem 5... The color of the card in my hand I have 4 black and 4 red cards. I would like to randomly draw the 1st card and then the 2nd card. Assume that each card has equal chance of being drawn on each draw and the cards are drawn without replacement) Let A: the 1st draw yields a red card B: the 2nd draw yields a red card Q1: What is the probability that 1st draw yields a red card? Q2: What is the probability that 2nd draw yields a red card? NUS/FoS/DSAP 10 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with Probabilities (Continued) Problem 5... The color of the card in my hand (Continued) Q2: What is the probability that 2nd draw yields a red card? NUS/FoS/DSAP 11 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with Probabilities (Continued) Problem 5... The color of the card in my hand (Continued) Q3: What is the probability that 1st draw yields a red card given that 2nd draw yields a red card? NUS/FoS/DSAP 12 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with Probabilities (Continued) Problem 5... The color of the card in my hand (Continued) √ You draw the 1st card and keep it without looking at the color of the card. The probability that it is a red card is _____. √ Now you draw a 2nd card and notice that it is red. Now, the probability that 1st draw yields red is _______. √ The probabilities above quantify your belief that the 1st card is red in various events. ☼ The additional information given has updated your degree of belief that you are having a red card in the 1st draw. NUS/FoS/DSAP 13 GEM2900 - Understanding Uncertainty & Statistical Thinking Semester 1, 2009/2010 How to Calculate with Probabilities (Continued) Problem 6... Revisit the game of craps We have talked about the rule of craps in lecture 9… So, what’s the chance of winning the game if we stop the game at a maximum of 2 throws… What’s the chance of winning the game of crap if we play with the rule of craps… stop till a win or loose is observed. NUS/FoS/DSAP 14...
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