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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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