## Friday, September 9, 2016

### "Given These Premises"....Inference

Am copying this verbatim from a recent Futility Closet posting about a hand of cards:

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Given these premises, what can you infer?
1. If there is a king in the hand then there is an ace, or if there isn’t a king in the hand then there is an ace, but not both.
2. There is a king in the hand.
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Now, go read the Futility Closet post:
As you will see, the post claims that “almost no one sees” the correct answer, and "practically everyone" infers (wrongly) instead that “there is an ace in the hand.”  The correct answer seems fairly obvious to me, but the post implies that most all fall for this “cognitive illusion.” Unfortunately there’s no way for me to know how many readers here immediately see the proper answer, but I’m wondering if math fans, perhaps more grounded in logic than the general populace, don’t answer this correctly at a much higher rate than other groups of people... IF that were indeed the case, it would be another indication of why training in mathematical thinking ought be encouraged.
The article says it is "unclear" why people mess up on this particular problem, though I think it's just one more example of how verbal cues are often very ambiguous or misleading for people... language is rarely as precise as individuals tend to assume. It all even reminds me a bit of a very old classic math conundrum that throws most people off (most of you will be familiar with it), which in one version (from Wikipedia) runs like this:
"Three people check into a hotel room. The clerk says the bill is \$30, so each guest pays \$10. Later the clerk realizes the bill should only be \$25. To rectify this, he gives the bellhop \$5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest \$1 and keep \$2 as a tip for himself. Each guest got \$1 back, so now each guest only paid \$9, bringing the total paid to \$27. The bellhop has \$2. And \$27 + \$2 = \$29 so, if the guests originally handed over \$30, what happened to the remaining \$1?"
OR, alternatively, here's a more recent example from the Web that many of you will recall, where the answer is actually fairly simple, yet many people, once again, are misdirected by the wording**:
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Jack is looking at Anne, but Anne is looking at George.
Jack is married, but George is not.
Is a married person looking at an unmarried person?

A) Yes       B)  No       C)  Cannot be determined
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...I s'pose the ability of language to hinder or interfere with rational thought has never been better demonstrated than by the current American presidential election :-(

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**  the correct answer is "A"