Question

The test to detect the presence of a liver disorder is 98% accurate for a person having the disease and 97% accurate for a person not having the disease. If in a given population, 3.5% of the people actually have the disorder, what is the probability that a randomly chosen person tests negative?
a) 0.93605
b) 0.93675
c) 0.965
d) 0.97035

Answer 1

I got D
0.97035
If you got a different answer please let me know.

Answer 2

How did you get that?

Answer 3

@TwoPointInfinity ^^

Answer 4

lets say you have 1,000 people
since 3.5% have the disease, that means 35 people have it and therefore the rest, 965 do not have it

Answer 5

of the 35 who have the disease, 98% will test positive, so .98×35=34.3 test positive
of the 965 who do not have it, 97% will test negative, and 3% will test positive
3% of 965 is .03×965=28.95 test positive

Answer 6

the total number that test positive is therefore 34.3+28.95=63.25

Answer 7

then divide by 1000 to get your probability

Answer 8

It's a lot easier to do this with numbers rather than with percents, although this is a probability question and we can use probabilities to solve it .

Answer 9

I think you actually helped me get the right answer, however I used decimals.
Since 96.5% of the population does not have it, I multiplied 0.965x0.97=0.9305
Because 97% is the accuracy of the test for people without the disorder.
Then since 3.5% of the population does have it, I multiplied 0.035x0.02=0.0007
Because 2% is the chance someone with the disorder will get the wrong result.
Then I added the two together to get 0.93675, which is b, but thank you for helping me kind of think how I would get that! @TwoPointInfinity