> The prescription put forward is simple. Essentially, we should all be using natural frequencies to express and think about uncertain events. Conditional probabilities are used in the first of the following statements; natural frequencies in the second (both are quoted from the book):
> The probability that one of these women [asymptomatic, aged 40 to 50, from a particular region, participating in mammography screening] has breast cancer is 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram.
> Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer?
> Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don't have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer?
https://plus.maths.org/content/reckoning-risk
> The prescription put forward is simple. Essentially, we should all be using natural frequencies to express and think about uncertain events. Conditional probabilities are used in the first of the following statements; natural frequencies in the second (both are quoted from the book):
> The probability that one of these women [asymptomatic, aged 40 to 50, from a particular region, participating in mammography screening] has breast cancer is 0.8 percent. If a woman has breast cancer, the probability is 90 percent that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7 percent that she will still have a positive mammogram.
> Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer?
> Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don't have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer?