Question

Suppose a particular woman tests positive; what is the probability that she has breast cancer?  

To pin this question , please consider a population in which 1% of women have breast cancer, and a mammography test which has a 90% chance of returning a correct result. That is, if a woman has cancer then there is a 90% chance the test will be positive, and if a woman does not have cancer then there is a 90% chance the test will be negative.

a smple of the population is 900

Answer 1

Answer)

Given sample size = 900

1% have cancer = 900*0.01 = 9

if a woman has cancer then there is a 90% chance the test will be positive,

True positive = 9*0.9 = 8.1

False negative = 9*0.1 = 0.9

if a woman does not have cancer then there is a 90% chance the test will be negative

True negative = 801.9

False positive = 89.1

Probability is given by favorable/total

Total = positive = 89.1 + 8.1 = 97.2

Favorable = has cancer = 8.1

Probability = 8.1/97.2 = 0.08333333333