Any test that has a probability of success less than 100 hundred perce

Question

Any test that has a probability of success less than 100 hundred percent leaves a researcher open to various types of errors. In one type of error, a test with some probability of success less than 100 percent has a chance of missing the true result equal to 100 percent minus the test’s percentage chance of success.

Which of the following inferences is most strongly supported by the information above?

A. If a test has a chance of success less than 100 percent it should not be used by a researcher.

B. There are no tests that have a success rate of 100 percent.

C. Researchers should use tests susceptible to error only when no perfectly reliable test is available.

D. If a test with a 95 percent chance of success indicates a negative result, there is a 5 percent chance the actual result is positive.

E. If a test with a 95 percent chance of success indicates a positive result, there is a 5 percent chance the test should have indicated a negative result.

Source:  McGraw-Hill's GMAT

Sajjad1994 · Accepted Answer

Official Explanation

The passage states that a test with a less than 100 percent chance of success will misinterpret the actual situation with a chance equal to 100 percent minus the success rate of a test. Thus, a test with a 95 percent chance of success has a 100 percent to 95 percent = 5 percent chance of misrepresenting reality.  Choice D  is thus supported by the passage.

Choices A  and  C  are not inferences because the argument doesn’t say what actions  “should”  be taken.

Choice B  is not supported by the passage and  choice E  misstates what the passage says; there is a 5 percent chance the result is wrong, not a 5 percent chance the test should have indicated something else.

Answer: D.

brunogr · Answer

Could someone explain what's difference between D and E?

Thank you!

dunghoang110 · Answer

I think E is incorrect because it says "should have indicated", meaning actually it doesn't indicate 5% true result, while the stimulus says it has the chance.

abhimahna · Answer

In D and E, I think only language of the answer choices makes the distinction. Can someone please provide their views? Does GMAT really test such kind of scenarios?

anje29 · Answer

Hi,
Please provide the explanation why D is correct not E

GMATNinja · Answer

This one is drawing a higher-than-normal number of requests for expert replies, but you might not like what I'm going to say: this question really doesn't sound like the GMAT at all to me. It sounds like the question writer was reading something about Bayes' Theorem, and decided to twist it into a GMAT CR question -- and I can't think of any official GMAT questions that even vaguely resemble this one. And the GMAT definitely doesn't test Bayes' Theorem!

Congrats to anybody who feels clear about the correct answer, but if you don't, don't worry about it. Feel free to use the tags to search for better, official questions.

Nightmare007 · Answer

This is a great question - 
 Here, NOTE - We should not bring outside knowledge which includes our previous experiences as it is an inference question .
We all have narrowed it to D and E.
 The stimulus saying that there is actually ( 100-x ) % chance that the TRUE RESULT is Distorted. 
Now in D : Says about chance of result being distorted.
In E : says that chance of Test giving other result.
IMO its D.

shakun · Answer

Neither of D and E can be inferred. 
Let's calculate D.
Pr  =  Pr  * \frac{Pr }{Pr }  = 5%* \frac{Pr }{Pr }

Now, the denominator, Pr  = Pr *Pr  + Pr *Pr  
=> Pr  = 95%*Pr  + 5%*Pr  = 95%*(1-Pr ) + 5% Pr  = 95% - 90%*Pr

Putting, Pr  = p
Original equation becomes, Pr  = 5%* \frac{p}{(0.95- 0.90*p)}

Which essentially means, 
  Pr  = 5% when +ve and -ve outcomes are equally likely (This is option D)
  Pr  > 5% when +ve outcome is more likely
  Pr  < 5% when -ve outcome is more likely

Hence we    cannot infer D    with confidence unless we know which outcome is more likely.

BTW, on a similar note,  we cannot say E  either.
Pr 
= Pr *Pr  + Pr *Pr 
= 0.95*(1-p) + 0.05*p = 0.95 - 0.90*p
Which means, Pr  = 5% when only +ve outcome can occur. Otherwise the probability will be greater than 5%.

Any test that has a probability of success less than 100 hundred perce

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GMAT Critical Reasoning (CR) Questions

Any test that has a probability of success less than 100 hundred perce

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