What is Mammography has 90% sensitivity and 98% specificity for breast carcinona. What is the probability that a woman with breast carcinoma remains undiagnosed for 2 consecutive years? and explain in detail?
Test is 90% sensitive, that means 90 out of 100 women with breast cancer will be diagnosed as breast cancer and 10 women with breast cancer will be undiagnosed.
So, probability that women with breast cancer will remain undiagnosed is 10/100 (1/10). However, this is true when test is used on time.
In second year, those 10 women (out of 100) will be screened once again as they were undiagnosed first time.
Probability to remain undiagnosed at second time is 10/100 or 1/10 (as the test is same)
So, out of 10 women (which were undiagnosed at first time) 9 will be diagnosed (as the sensitivity of test is 90%) and 1 will remain undiagnosed at second examination.
Thus, after second examination 1 out of 100 women with breast cancer will remain undiagnosed.