Probability question

[gadad]

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I'll admit it, I'm dumb as a brick when it comes to stats; even basic stuff.

There's a question about probabilities in a Q-bank that I use; I searched around some, but cannot figure it out. Honestly, I don't want to spend anymore time on it, but it is bugging me.

Please teach me:

Q (changed around some):

A test is negative in 90% of patients who do not have the disease. If the test is used in 9 consecutive blood samples taken from patients without the disease, what is the probability of getting at least one positive test result?

A= 1-0.90^9

My question is, why isn't it 0.10^9 (that was also an answer choice).

I understand why 1-0.90^9 is correct (at least superficially); I just do not understand why 0.10^9 isn't.

[I understand that since addition/subtraction is involved, they CANNOT both be correct; I just don't understand why I need to pick 1-0.90^9 over 0.10^9]

Any help will be appreciated.

 

[dotdash]

A test is negative in 90% of patients who do not have the disease. If the test is used in 9 consecutive blood samples taken from patients without the disease, what is the probability of getting at least one positive test result?

A= 1-0.90^9

My question is, why isn't it 0.10^9 (that was also an answer choice).

Just thinking about the problem logically, the probability of finding at least one false positive has to go up the more people you test. So you have to combine the probabilities in such a way that the answer gets larger as you do more trials. As you raise .10 to higher powers, it gets smaller so that can't be the answer (it is, in fact, the probability of getting ALL false positives). (1-(.9^x)), however, gets larger as the x increases.

From a mathematical point of view, what you are first calculating is the probability you will get get all correct rejections of the test (90% probability). That's the .9^x term, which gets smaller as x increases. Then you subtract that number from 1 to get the probability of having at least 1 false positive, which gets larger as the second term gets smaller.

Good luck!

 

[gadad]

...As you raise .10 to higher powers, it gets smaller so that can't be the answer (it is, in fact, the probability of getting ALL false positives).

...From a mathematical point of view, what you are first calculating is the probability you will get get all correct rejections of the test (90% probability). That's the .9^x term, which gets smaller as x increases. Then you subtract that number from 1 to get the probability of having at least 1 false positive, which gets larger as the second term gets smaller.

Ok, I get it now. I was not distinguishing ALL false positives from 1-false positive. I knew that 0.10^9 would give me the false positive rate, I just wasn't thinking that they were only asking for 1-false positive; I need more sleep!!!

Thanks!

 

[PokerDoc]

Am I the only one who thinks it's beyond obnoxious that this kind of question can show up?

 

[Rabbit Hole]

Am I the only one who thinks it's beyond obnoxious that this kind of question can show up?

Probably.

 

[kryptik]

only 25% of people got a simiar question right in UW, question id 1284