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#1




What's the probability of getting at least one positive result?
New test is 95% negative on patients who do not have the disease. If test is used in 8 healthy volunteers, what is the probability of getting at least one positive result?
a) 1 0.05 X 8 b) 0.05 X 8 c) 0.05 ^ 8 d) 0.95 ^ 8 e) 1  0.95 ^ 8 ^ means degree (like 2^3=8) 
#2




should be E
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nothing is impossible! 
#3




The answer is E) 1  0.95 ^ 8
Explanation: Short version P(+) = p = 0.05 P() = q = 0.95 n = 8 The probability of getting AT LEAST one positive = P(X>=1) This is the same as: 1  P(X=0) = 1  0.95^8 P(X=0) = always q^n  Long version This follows a Binomial distribution, where: P(X=0) = nCr * p^r * (q)^(nr) P(X=0) = (n combinations r) * p^r * (q)^(nr) P(X=0) = 8C0 * 0.05^0 * (0.95)^(80) P(X=0) = 1 * 0.95^8 = 0.95^8 Last edited by bebix; 07312011 at 11:54 AM. Reason: sorry...should say "always q^n" and NOT p^n 


#4




Quote:

#5




Quote:
The probability of getting ALL positive results c) 0.05 ^ 8 => P(X=8) The probability of getting AT LEAST one positive result e) 1  0.95 ^ 8 => P(X>=1) 
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pass7 (07312011) 
#6




E.) 1all negative= at least one positive
please correct me if i am wrong. 
#7




Quote:
E is correct; Heard the concept in lecture, but got wrong 'could not apply'. 
#9




Quote:
P(X=0) = always p^n Could you please explain this bit in words? I am not able to follow this concept. 
#10




Quote:
P() = q = 0.95 n = 8 P(X=0) = Probability of getting ALL negative results P(X=0) = always q^n (this is a fact!!!...now, if you really really want to understand why this is always true, just read the explanation below about binomial distribution and probabilities!)  This follows a Binomial distribution, where: P(X=0) = nCr * p^r * (q)^(nr) P(X=0) = (n combinations r) * p^r * (q)^(nr) P(X=0) = 8C0 * 0.05^0 * (0.95)^(80) P(X=0) = 1 * 0.95^8 = 0.95^8 ==> q^n  Then, the probability of getting AT LEAST one positive is equal to: P(X>=1)...and this is ALWAYS the same as 1  P(X=0). Finally, at least one will be equal to => 1  q^n => 1  (0.95)^8 For more about binomial distribution http://en.wikipedia.org/wiki/Binomial_distribution 
The above post was thanked by:  
donofitaly (08012011) 
Tags 
BiostatisticsEpidemiology, Step1Questions 
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