#25 - A letter submitted to the editor of a national

[josuecarolina]

This one has to do with a medical professional who writes a magazine and mentions that they (the author) is a professor at a north american medical institution. The argument is then made that because less than %5 of people in those institutions is a woman, there is a 95% likelihood that the author is a man.

I don't understand what the flaw is in the reasoning here. Help? thanks!

[Steve Stein]

Hi,

That's an interesting question. If 95% of the employees are men, that means that if we were to pick one, at random, without knowing anything else about them, then we could say that there was a 95% chance that the person was a man. In this case, however, the doctor's first name is Shirley--this is no longer a random draw--there must be better than 1 in 20 shot that this person is a woman, because there are almost no men with that name.

Similarly, the correct answer choice provides that only one animal in 20 in a certain preserve is a bird. Even so, if we see something flying, we know that there is a better than 1 in 20 chance that the animal is a bird, because the fact that is was flying rules out most mammals (in much the same way as having the name "Shirley" rules out almost all men).

I hope that's helpful! Let me know--thanks!

~Steve

[josuecarolina]

Shirley you jest! Seriously, this question sucks. Thanks.

[biskam]

I'm confused with the language of a ratio... what does 19 to 1 mean... is that equivalent to a 95% chance?

thank you!

[biskam]

Doesn't the author in the stimulus have a better chance of shirley being a female, given presumably her name? So why does the author conclude that he has better chances that it's written by a man? is that part of the flaw?

and with the correct answer choice, wouldn't the author presume that the animal was a bird rather than a mammal since it was flying??

[Adam Tyson]

That is indeed the flaw, biskam - the author in the stimulus has failed to take into account something that is known beyond just the pure numbers. We need an answer that shows someone also failing to take into account something other than just the numbers. In the stimulus, the author failed to take into account the likelihood of someone named Shirley being male (low, but not impossible), and in answer E the author failed to take into account the likelihood of a flying creature being a mammal (low, but not impossible). That's the same flaw - the "failing to take into account another important piece of data".

Since the stimulus asked you to find the answer with the same flaw, start by identifying the flaw (hey, isn't it more likely that a person named Shirley is female?) and find the answer with the same flaw (hey, isn't it more likely that a flying creature is a bird?).

19-1 is the same as 95-5, or a 95% probability, by the way - just multiply those numbers by 5 and you're there!

There will be more questions to come that involve these numbers and percentages issues, biskam, so practice them often. It'll pay off. Count on it!

[biskam]

Got it! The author is ignoring the fact that he/she knows that Shirley is a female (given her name, nonnumerical data) and that the animal was a bird (given the wings, nonnumerical data) and is instead foolishly focusing on pure number stats that tell them 95% of doctors are men and 19/20 animals are mammals, making conclusions based solely on those numbers. Thanks!!