Sat Guessing

[eagle_eye222001]

[url="http://what-if.xkcd.com/2/"]http://what-if.xkcd.com/2/[/url]


[color=#005994][font=Verdana, Helvetica, Arial, sans-serif][i]What if everyone who took the SAT guessed on every multiple-choice question? How many perfect scores would there be?[/i][/font][/color]
[right][i]—Rob Balder[/i][/right]



[color=#000000][font=Georgia, Times, serif][spoiler]None.[/font][/color]
[color=#000000][font=Georgia, Times, serif]The SAT is a standardized test given to high school students (similar to the ACT). The scoring is such that under certain circumstances, guessing an answer can be a good strategy. But what if you guessed on everything?[/font][/color]
[color=#000000][font=Georgia, Times, serif]Not all of the SAT is multiple-choice, so let’s focus on the multiple choice questions to keep things simple. We’ll assume everyone gets the essay questions and fill-in-the-number sections correct.[/font][/color]
[color=#000000][font=Georgia, Times, serif]There are 44 multiple-choice questions in the math (quantitative) section, 67 in the critical reading (qualitative) section, and 47 in the newfangled writing section. Each question has five options, so a random guess has a 20% chance of being right:[/font][/color]
[img]http://what-if.xkcd.com/imgs/a/2/01.png[/img]

[center][color=#000000][font=Georgia, Times, serif]Although we all know the answer is always B.[/font][/color][/center]

[color=#000000][font=Times New Roman][size=4]The probability of getting all 158 questions is:[/size][/font][/color]


[left][color=#000000][font=Times New Roman][font=MathJax_Main]1[/font][font=MathJax_Main]5[/font][font=MathJax_Main]44[/font][font=MathJax_Main]∗[/font][font=MathJax_Main]1[/font][font=MathJax_Main]5[/font][font=MathJax_Main]67[/font][font=MathJax_Main]∗[/font][font=MathJax_Main]1[/font][font=MathJax_Main]5[/font][font=MathJax_Main]47[/font][font=MathJax_Main]≈[/font][font=MathJax_Main]1[/font][font=MathJax_Main]2.7[/font][font=MathJax_Main]∗[/font][font=MathJax_Main]10[/font][font=MathJax_Main]110[/font][/font][/color][/left]


[center][color=#000000][font=Georgia, Times, serif](That's one in twenty-seven quinquatrigintillion.)[/font][/color][/center]

[color=#000000][font=Georgia, Times, serif]If all four million 17-year-olds all took the SAT, and they all guessed randomly, it’s a statistical certainty that there would be no perfect scores on any of the three sections.[/font][/color]
[color=#000000][font=Georgia, Times, serif]How certain is it? Well, if they each used a computer to take the test a million times each day, and continued this every day for five billion years—until the Sun expanded to a red giant and the Earth was charred to a cinder—the chance of any of them ever getting a perfect score on [i]just the math section[/i] would be about 0.0001%.[/font][/color]
[color=#000000][font=Georgia, Times, serif]How unlikely is that? Each year something like 500 Americans are struck by lightning[sup][url="http://www.uic.edu/labs/lightninginjury/Disability.pdf"][1][/url][/sup][sup][url="http://www.nws.noaa.gov/om/hazstats/light08.pdf"][2][/url][/sup] (based on an average of 45 lightning deaths and a 9-10% fatality rate). This suggests that the odds of any one American being hit in a given year are about one in in 700,000 (although probability can be [url="http://xkcd.com/795/"]tricky[/url]).[/font][/color]
[color=#000000][font=Georgia, Times, serif]This means that the odds of acing the SAT by guessing are worse than the odds of every living ex-President and every member of the main cast of Firefly all being independently struck by lightning … [i]on the same day[/i].[/font][/color]
[img]http://what-if.xkcd.com/imgs/a/2/03.png[/img]

[center][color=#000000][font=Georgia, Times, serif](Everyone survives but Alan Tudyk and Ron Glass)[/font][/color][/center]

[color=#000000][font=Georgia, Times, serif]To everyone taking the SAT this year, good luck—but it won’t be enough.[/spoiler][/font][/color]

[Slappo]

Maybe we'll get lucky and the lightning thing will happen . Can we change it to every cabinet member in the current administration though, and make them non-life threatning injuries?

Edited July 11, 2012 by Slappo

[tinytherese]

I've always done terribly on standardized tests and loathe them with a passion. I never took the SAT, but the ACT three times. My highest score was an 18. Yet when it comes to how I do in class, since high school I've averaged a 3.6 GPA.

[CatherineM]

I took the ACT twice.

[brianthephysicist]

My SAT's were pretty good, somewhere in the 1300's out of 1600 but my ACT's were a near perfect 34 out of 36. My brother, on the other hand, did somewhere in the 1200's out of 1600 for the SAT's but his ACT's were a terrible 14 out of 36.

Different thinking styles (even for people with similar backgrounds like my brother and I) are better suited for different tests. That's why I don't like standardized testing. I lucked out that they made a test the way I happen to think, but someone could easily have designed the test to target a completely different type of thinking style.

[i<3franciscans]

I have a 4.0 gap and got a 1700 on the SAT. I am taking it again in oct.

[Amppax]

The one about baseball was better.

[CatherineM]

I did 42 on the LSAT

[carmenchristi]

Does it have to be limited to only the ex presidents getting stuck by lightning????