Question

Complex Decisions Using Probability
The test to detect the presence of the hepatitis B virus is 97% accurate for a person who has the disease and 99% accurate for a person who does not have the disease. If 0.55% of the people in a given population are infected, what is the probability that a randomly chosen person gets an incorrect result?

0.98455

0.000165

0.009945

0.001011

Answer 1

bayes formula i guess

Answer 2

ive never seen that in my textbook

Answer 3

which is often confusing, so the best way to do this is make up actual numbers
then it will be clearer
since .55%=.0055 is a very small number, lets take a huge sample size

Answer 4

ok

Answer 5

say one million 1,000,000

Answer 6

now .55% have the disease so that makes \(5500\) have it a the rest do not

Answer 7

that means \(994500\) do not have the disease

Answer 8

ok but this has 2 percents and no numbers

Answer 9

yeah we are getting there

Answer 10

so \(994500\) do not have the disease, and the test is 99% accurate for them, so 1% of them get a wrong reading, i.e. \(9945\) get an incorrect reading among the people that do not have the disease

Answer 11

\(5500\) people have the disease, and 3% of them get the wrong reading, i.e. \(165\) people get the wrong reading

Answer 12

the total number of people who get the wrong reading is therefore \(9945+165=10110\)

Answer 13

now take that number as a percent of the 1,000,000 people total

Answer 14

of course you can do the same calculation without making up the 1,000,000 population, and just work with a bunch of decimals
the calculation is identical, it just usually makes more sense if you pick a large imaginary sample size and figure out what it would be from that

Answer 15

ok