《那些古怪又讓人憂心的問題》第136期:考試靠猜
SAT GUESSing
Q. What if everyone who took the SAT guessed on every multiple-choice question? How many perfect scores would there be?
Q．如果每個參加美國高考（SAT）的學生都在選擇題部分亂猜一氣會怎麼樣？有多少人會獲得滿分？——Rob Balder
——羅布•鮑爾德
A. NONE.
A．沒人。The SAT is a standardized test given to American high school students. The scoring is such that under certain circumstances, guessing an answer can be a good strategy. But what if you guessed on everything?
SAT考試是給美國高中學生參加的標準化測試，在一些情況下，亂猜一個答案是一個不錯的選擇。但如果你所有題目都亂猜呢？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.
SAT考試並非全部都是選擇題，爲了把問題簡單化，我們假定只在選擇題部分亂猜答案，並假設所有人在寫作題目和填空部分都拿了滿分。In the 2014 version of the SAT, there were 44 multiple-choice questions in the math (quantitative) section, 67 in the critical reading (qualitative) section, and 47 in the newfangled1 writing section. Each question has five options, so a random guess has a 20 percent chance of being right.
在2014年的SAT考試中，數學部分有44道選擇題，批判性閱讀部分有67道，新式1的寫作部分有47道。每道選擇題有5個選項，因而亂猜一個答案有20％的機率能夠猜對。The probability of getting all 158 questions right is:
所有158道選擇題都猜對的機率爲：If all four million 17-year-olds took the SAT, and they all guessed randomly, it's a virtually certain that there would be no perfect scores on any of the three sections.
如果全部400萬17歲的孩子都去參加SAT考試瞎猜答案，那麼幾乎可以肯定的是，在三個部分中的任何一個部分都不會有滿分出現。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 just the math section would be about 0.0001 percent.
有多肯定？假設他們每天用計算機參加100萬次考試，並且持續50億年——直到太陽膨脹成一顆紅巨星，將地球燒成渣——在這麼多次考試中，僅僅數學部分得到滿分的機率只有萬分之一。How unlikely is that? Each year something like 500 Americans are struck by lightning (based on an average of 45 lightning deaths and a 9–10 percent fatality rate). This suggests that the odds of any one American being hit in a given year are about 1 in 700,000.2
這機率有多小？每年有大約500名美國人被閃電擊中（平均每年有45人死於雷擊，被雷擊的死亡率約爲9％～10％）。這意味着指定某一年任選一個美國人，他被閃電擊中的機率是七十萬分之一。2This 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 . . . on the same day.
這意味着如果想通過亂猜獲得SAT考試滿分，這個機率比所有健在的前總統加上《螢火蟲》3的全部主演們都在同一天被閃電擊中的機率還小。To everyone taking the SAT this year, good luck-but it won't be enough.
致今年參加SAT考試的各位，祝你們好運啦——雖然光靠運氣是沒用的。1 I took the SAT a long time ago, okay?
1． 很久以前我考過SAT考試，行了吧？
