Probability Question: 10% Smoke Marihuana, 8 People Tested

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This is not to say that the person who did test positive is not likely to be a pot smoker, just that given the one data point, it is 50/50 that he is.)In summary, the conversation discusses a probability question about testing for marijuana use. It is determined that the chance of a person actually smoking marijuana, given that they tested positive, is 50%. This calculation is not dependent on the total number of people being tested.
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martine
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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
 
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90%?
 
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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%.
 

1. What is the probability that a person smokes marijuana based on this information?

The probability is 10% or 0.1. This means that out of a sample of 8 people, it is expected that approximately 1 person will smoke marijuana.

2. How was the 10% probability calculated?

The 10% probability was calculated by dividing the number of people who smoke marijuana (1 person) by the total number of people in the sample (8 people).

3. Can this probability be applied to a larger population?

It is not recommended to apply this probability to a larger population without further research. This sample size is too small to accurately represent the entire population.

4. What is the margin of error for this probability?

Since this is a small sample size, the margin of error may be high. It is recommended to conduct further research with a larger sample size to reduce the margin of error.

5. How does this 10% probability compare to national statistics?

This probability may differ from national statistics as it is based on a small sample size and may not accurately represent the entire population. It is important to consider the source and methodology of the national statistics when comparing them to this probability.

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