- #1
daigo
- 27
- 0
So here is the typical question:
I know that Bayes' Theorem should be applied here, but I don't understand why. I am going to pretend I don't know the formula and try to solve this, but I can't seem to get it:
W = Women in age group 40
B = Has Breast cancer
P = Positive tested for breast cancer
.01W = B
(.8B)W = P
(.096[W - B])W = P
Since 1% of women in this age group have breast cancer,
80% of those with breast cancer in this age group have positive mammographies,
and 9.6% of those without breast cancer in the age group also have positive mammographies.
I solved for W, B, and P and got 9.333 (repeating), .09333 (repeating), and .0696888 (repeating) respectively.
So the probability of having breast cancer from a positive mammography would be: .09333 / .0696888, no? But obviously that isn't the correct answer since that's over 100% chance.
How does one work this out intuitively? I don't even understand how the Bayesian formula is derived for this type of problem. I understand that I have to use it and why it works, but not why I have to use it and why I have to apply it.
1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
I know that Bayes' Theorem should be applied here, but I don't understand why. I am going to pretend I don't know the formula and try to solve this, but I can't seem to get it:
W = Women in age group 40
B = Has Breast cancer
P = Positive tested for breast cancer
.01W = B
(.8B)W = P
(.096[W - B])W = P
Since 1% of women in this age group have breast cancer,
80% of those with breast cancer in this age group have positive mammographies,
and 9.6% of those without breast cancer in the age group also have positive mammographies.
I solved for W, B, and P and got 9.333 (repeating), .09333 (repeating), and .0696888 (repeating) respectively.
So the probability of having breast cancer from a positive mammography would be: .09333 / .0696888, no? But obviously that isn't the correct answer since that's over 100% chance.
How does one work this out intuitively? I don't even understand how the Bayesian formula is derived for this type of problem. I understand that I have to use it and why it works, but not why I have to use it and why I have to apply it.