Easy question? What is the probability that a person who tests negative has leukemia?
Easy question? What is the probability that a person who tests negative has leukemia?
A medical test for leukemia is 97% accurate. Suppose 0.6% of the population have leukemia. What is the probability that a person who tests negative has leukemia?
APPARENTLY.. the answer is 0.000187
Which I think is wrong.. Isn't it just 3%? Pretty much no math involved it seems. Can someone find out where the 0.000187 comes from?
Please show your work :) Thanks !!
- David H
"Which I think is wrong.. Isn't it just 3%."
Nope.
The probability of a false negative is 3% and the probability of a true negative is 97%. The probability a person has leukemia is 0.6% the probability they don't have it is 0.994%.
Four outcomes are possible
1. Positive, No Leukemia (P = 0.994*0.03 = 0.02982)
2. Positive, Leukemia (P = 0.006*0.97 = 0.00582)
3. Negative, No Leukemia (P = 0.994*0.97 = 0.96418)
4. Negative, Leukemia (P = 0.006*0.03= 0.00018)
0.00018/(0.96418 + 0.00018) = 0.001867
- kelby7670
An easy way to look at it.
Start with 1000000 people.
6000 have leukemia
994000 do not
Of the 6000 who have leukemia , 180 test negative (because the test is wrong .03 of the time
Of the 994000 who do not have leukemia, 964180 will test negative because the test is right 0.97 of the time
A total of 964360 test negative
Of those 964360, 180 have leukemia
So the answer is 180/964360
Leukemia — Comprehensive overview covers symptoms, causes, risk factors, treatment of this blood-related cancer.
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