Help with probability! :(

[Papi]

Hi everyone,

When I took the MCATs last year, there were FOUR probability free questions on there that I did not know how to answer, for some reason, none are in the AMCAS VI.

I was wondering if someone could help me questions like these:

There are 200 men, 65% of whom have disease A. A scientist invents a test that can detect this particular disease A with a accuracy of 45%.

How many of the men tested actually had disease A but went undetected?

Would it just be 200 x .65 . 45 ?

Also, does anyone have a good site on how to approach probability questions? Thanks!

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[Engg to Doc]

Hi,
I am not too sure about this, but I'll post my guess here:

65% of 200 people had disease A. So 130 people had it.
45% of 200 people could be detected by the test, so 90 people were diagnosed with having disease A.
Out of the 130 who had it, only 90 were diagnosed, so 40 people who had it went undetected.

I don't know if it is this trivial, but it does not look like probability to me, looks like simple percentage - But that is an engineer talking! Don't go by my guess - I am a long way off from taking the MCAT. Maybe some experts could look into this solution....

 

[I to A]

[

There are 200 men, 65% of whom have disease A. A scientist invents a test that can detect this particular disease A with a accuracy of 45%.

How many of the men tested actually had disease A but went undetected?

Would it just be 200 x .65 . 45 ?

Answer:
130 have the disease.

When the test is done on these 130 people, 45% will be detected, i.e., in 58.5 men (or 59) it will be detected and in 71 it will go undetected.

Your method, gives 58.5, the no. that the test detects, but the questions wants the no. that went undetected. Answer is 71 men.

Hope it helps.

 

[Mr. Z]

Good question Papi

I'm not sure if i'm right, but here is how i would approach it:

65% of 200 have the disease, that means 130 people have the disease.

We have a test which has 45% accuracy. This means that 55% of the time people who have the disease go undetected.

so 55% of 130 is 71-72, which would be the number of false negatives (people with the disease who test negative for it).

Can somebody double check this for me? not certain about it.

 

[Engg to Doc]

Actually,
The above 2 posts seem to make more sense. The answer should be: 200 X .65 X .55

My mistake was that the sampling size for the second part of the problem should not be 200, but 130.

 

[Mr. Z]

Papi, what other types of probability questions did you see? can you give us some examples. This is something i haven't yet considered.