Question

The test to detect the presence of a liver disorder is 98% accurate for a person who has the disease and 97% accurate for a person who does not have the disease. If 3.5% of the people in a given population actually have the disorder, what is the probability that a randomly chosen person tests positive?

0.0343

0.035

0.06325

0.02895

Answer 1

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

Answer 2

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 3

but then what about the 97% and 98%?

Answer 4

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

Answer 5

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

Answer 6

then divide by 1000 to get your probability

Answer 7

thank you!

Answer 8

yw