Consider a test for illegal drugs that is 98% accurate. Lets test 3000 poeple, 2900 of whom do not use illegal drugs.
What percent of the total positive tests were false?
What is the chance of a person testing falsely positive twice in a row?
of the 3000, you would expect postives from
2900(.98)+100(.02)
2842+2=2844
percent total false positives: 2/2844 x100
change same person twice?
Pr=(2/100)(1/100)
check my thinking, it is early in the morning.