Probability Question: 10% Smoke Marihuana, 8 People Tested

[martine]

Hi all,

I think this would be a probability question.

We do a random check. 10% smokes marihuana. This test gives the right results in only 90%. One person is tested positive. How big is the chance that he really smoked marihuana?
-if there are 8 people in total.
-is it also possible to make an assumption if the size of the group is not known?

thanks a lot!

Martine

 

[phoenixthoth]

90%?

 

[HallsofIvy]

Since everything is given in terms of percentages, the actual total number is irrelevant.


Suppose there were 100 people tested. Assume that 10% of them (10) actually smoke marijuana, 90 do not.

The test is 90% accurate (I assume that is both 10% false positives and 10% false negatives- often those are two different numbers).

Of the 10 people who actually do smoke, 9 will test positive and 1 negative.

Of the 90 people who do not, 81 will test negative and 9 positive so that we have a total of 18 positives and 82 negatives.

Given that a person tested positive, he/she is in that group of 18 positives. Of those, actually only 9 were actuall pot smokers so the probability that a person actually smokes marijuana, given that he/she tested positive, is 50%.