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Reality-Based Thinking Quiz
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Question 1
A bat and ball sell together for a total cost of $1.10. The cost of the bat is $1.00 more than the cost of the ball.
What is the cost of the ball?
A
$ 0.05
B
$ 0.10
C
$ 0.50
D
$ 0.75
E
$ 1.00
Question 1 Explanation:
The ball costs $ 0.05. The bat is $1.00 more than the ball, or $1.05. When added together, $ 0.05 and $ 1.05 equal $1.10.
A strong majority of respondents answer that the ball is $ 0.10. This is an incorrect answer that could easily have been discovered ahead of time simply by checking the math before giving a final answer.
This classic problem is an excellent example of "framing" and the mind finds it very easy to offer up the "$ 0.10" answer as coherent. Here's how the framing works:
Think of the question this way: A bat and ball sold together cost A DOLLAR and TEN CENTS. (You just got "framed" with two values. And now the question continues....) The bat costs A DOLLAR (remember that value? Now you've heard it twice.) more than the ball. How much is the ball.
Well, you've already heard "A DOLLAR" twice, and you've only heard "TEN CENTS" once. So your mind suggests the value of "ten cents". This suggestion feels right because there's something coherent about it. But it's not the right answer!
Question 2
Jack is looking at Anne, but Anne is looking at George. Jack is married. George is unmarried.
Is a married person looking at an unmarried person?
A
Yes
B
No
C
Cannot be determined
Question 2 Explanation:
About 80% of people answer this question with "cannot be determined", but this is incorrect. Yes, it's true that we do not know Anne's marital status. And those who answer #3 are most likely thinking about that. What they did not discover, however, is that it turns out that we do not need to know Anne's marital status. It happens to work out that a married person is looking at an unmarried person in this scenario whether Anne is married or not.
Question 3
Larry is a quiet, fastidious, and organized man who loves to read and to help other people.
Which is more likely to be Larry's profession?
A
Farmer
B
Librarian
Question 3 Explanation:
Larry could be either a farmer or a librarian, of course, but it is more likely that he is a farmer. Many people mistakenly assert that Larry is more likely to be a librarian because the details given about Larry (quiet, fastidious, organized, loves to read, loves to help people) make for a very coherent story if Larry is a librarian. There are a great many more male farmers than male librarians*, however, and this statistic should be taken into account when formulating an answer about the likelihood of Larry's profession.
* In the US, there are about 34,000 male librarians, and over 1.8 million male farmers.
Could a farmer meet Larry's description? Sure, he could. In fact, for all we know, Larry always wanted to be a librarian, but took over the family farm out of a sense of responsibility.
This problem is an example of what is called "base rate neglect"---neglecting to take into account general statistics relevant to the question at hand.
Question 4
This is a fact about the cards below: each has a letter on one side and a number on the other. Here is a rule about these cards that needs to be tested: If a card has a vowel on one side, it has an even number on its reverse.
Which card or cards must you turn over in order to test whether this rule is true or false?
A
A and 8 only
B
A and 5 only
C
All four cards
D
K only
E
K, A, and 8 only
F
None of the above
Question 4 Explanation:
In order to test the rule, you must turn over the A card and the 5 card. Turning the K and 8 are not necessary. Here are discussions on each individual card:
K. Turning the K card does not help because we know that each card has a letter on one side and a number on the other. The rule concerns only those cards with a vowel on the letter side. So turning the K card does not help us test the rule.
A. Turning the A card is necessary because we know it has a number on the reverse, and we can check to see whether that number is even (following the rule) or odd (breaking the rule.)
8. Turning the 8 card is nearly irresistible for many, but it does not test the rule. Most who want to turn it are curious as to whether there is a vowel on the reverse, and if there is not, they will believe that the rule has been violated. The cognitive error in play here, however, is that the real rule (“if vowel, then even”) is being replaced with its reverse (“if even, then vowel”). That is, people assume that if we have an even number on the number side (the 8), then the rule requires a vowel on the opposite side. If-then statements, however, are only intended to tell us something in a left-to-right order; they are not intended to read backwards. In other words, “If A, then B” is not meant to convey also that “If B, then A”. If the 8 card (an even) has a consonant on the reverse, that does not prove or disprove the rule, because the rule is not “If even, then vowel”, but “If vowel, then even.”
5. Turning the 5 card is necessary because it might test the rule. If it has a consonant on its reverse, we learn nothing of value in testing the rule, but if it has a vowel on its reverse, then we would learn that the rule is false, for we are told that any card with a vowel on one face must have an even number on the other.
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You missed all four questions for a score of 0%. Don't worry, our founder missed three of these four questions the first time he saw them, and that's why he started the Society! Missing these doesn't mean that you're stupid, but only that you didn't put enough thinking into your answers or that your method of thinking needs some tweaking. The great news is that with just a little bit of learning and some good old-fashioned effort, you can learn to get questions like these right most of the time! Please keep reading the website to see how we can help.
You missed three of the four questions for a score of 25%. Don't worry, that's the same score our founder got the first time he saw them, and that's why he started the Society! Missing these doesn't mean that you're stupid, but only that you didn't put enough thinking into your answers or that your method of thinking needs some tweaking. The great news is that with just a little bit of learning and some good old-fashioned effort, you can learn to get questions like these right most of the time! Please keep reading the website to see how we can help.
You missed two of the four questions for a score of 50%. Believing it or not, this "failing" grade is better than most people score on this quiz! Don't worry, our founder only got one of four right the first time he saw them, and that's why he started the Society! Missing these doesn't mean that you're stupid, but only that you didn't put enough thinking into your answers or that your method of thinking needs some tweaking. The great news is that with just a little bit of learning and some good old-fashioned effort, you can learn to get questions like these right most of the time! Please keep reading the website to see how we can help, as well as to see how YOU can help others improve their thinking, too!
You missed one of four questions for a score of 75%. That's way better than the average person does! Don't worry, our founder missed two of these three questions the first time he saw them, and that's why he learned how to do better, and then started the Society to help others! Please keep reading the website to see how we can help with whatever you missed, as well as to see how YOU can help others improve their thinking, too!
Great work! You went above and beyond the level of thinking most people conjure up in answering these questions. Not only did you try harder than most, but you also avoided the erroneous methods of thinking that cause most to fail on these particular questions. Have you seen them before, or did you simply determine to try really hard?
The real challenge for us now is to determine whether you are always "on it" like this, or whether your performance in this quiz is just a fluke. Further, our society is plagued with poor thinking, and we want you to consider joining SRBT to help promote reality-based thinking. Please keep reading the website to see how we can help together.
We missed most of these questions, too—and just like you, we were surprised to learn that our everyday thinking was not always based in reality. So that’s why we started the Society for Reality-Based Thinking—to help people learn to avoid the common errors we all tend to make. Reality-Based Thinking (RBT) is not all that hard to do, and once you get the hang of it, you realize that the whole world could make good use of it. But for now, let us suggest a much more modest goal: What if you could improve your own judgment and decision making enough to cut down your errors to 50% of their current level? How much time, money, heartbreak, and frustration would that save you?
We believe that RBT can do just that for you—provided you put forth the effort to learn it and to use it. You can try more problems here at any time. But please be sure to read next about how messed-up the world’s thinking is!
