Question

**WILL FAN & MEDAL**
I need help with this problem
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?
A) 0.0343
B) 0.035
C) 0.06325
D) 0.02895

Answer 1

Hii!

Answer 2

HI!!

Answer 3

lets do it with numbers !

Answer 4

or not maybe @Astrophysics has a better way

Answer 5

It's cool you can go ahead :)

Answer 6

i would start by saying lets test 10,000 people

Answer 7

\[3.5\%\] of them have the disease, and \[3.5\%\] of \(10,000\) is \(350\) so \(350\) people have it

Answer 8

\[98\%\] of those 350 will test positive, and \[0.98\times 350=343\]so we know that 343 people who have it will test positive

Answer 9

now lets see how many of those who do not have it will test positive
first off, 350 have it so \[10,000-350=9650\] so not have the disease
of those \(3\%\) will also test positive

Answer 10

\[.03\times 9650=289.5\] so \[289.5\] will of those who do not have it will also test positive

Answer 11

all together, how many people test positive?

Answer 12

i.e. add \[289.5+343\]

Answer 13

632.5?

Answer 14

ok, then divide by \(10,000\) by moving the decimal over to get your answer

Answer 15

0.06325?

Answer 16

oh imagine that! the answer is once again C
when in doubt, charlie out

Answer 17

Thanks a lot for your help, you explained it very well :)

Answer 18

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