Jim Worthey • Lighting & Color Research • jim@jimworthey.com • 301-977-3551 • 11 Rye Court, Gaithersburg, MD 20878-1901, USA
 How Do You Feel About Logic?

Here are two related brain teasers. The answers are given farther down the page. If these problems are new to you, please try carefully to get the answers, then check your answers and read the explanation. Pay attention to the feelings that you have, or recall your feelings when you first saw questions similar to these.

Brain Teasers:

1. You know that a family has 2 children. You learn that the older child is a girl. Now what is the probability that the other child is a girl?

2. You know that a family has 2 children. You learn that at least one of them is a girl. What is the probability that the other child is also a girl?

— Please work both problems, then scroll down for the answers —

 Answer to Question #1 The older child is a girl. The probability that the other child is a girl is 1/2.

— keep scrolling for the next answer —

 Answer to Question #2 At least one child is a girl. Now the probability that the other child is a girl is 1/3.

— keep scrolling —

Explanation

Both problems: if you have no information except that there are 2 children, then there are 4 possible cases:

 A B C D Older girl girl boy boy Younger girl boy girl boy

1. If you are told that the older child is a girl, then the possibilities are only A and B. The probability of case A (2 girls) is one out of two, or 1/2.

2. If you are told that at least one child is a girl, this excludes case D. The possibilities are A, B, and C, and only in case A is the second child a girl. This is 1 case out of 3, so the probability is 1/3.

Discussion

How did you feel the first time that you saw these puzzles, whether today or earlier?
Just look at the 2 questions. Does the first question seem dumb? Why does the girl's age matter? Is a big girl more likely to have a sister than a little girl?

You are welcome to your feelings, whatever they are, but consider this thought. The problems may be quite mysterious when you first encounter them. When you see the logical answer, it works by taking the mystery out of the problem.

It may appear at first that the problem of the two children is a trivial amusement. The setup is simple and you could ask the older sister what her sibling's gender is. In reality, this is an important example for a course in probability. For instance, it can be viewed as speaking to the notion of independent events. If you know only that there are two children, then the sex of the older and the sex of the younger are independent events. If you are told that "at least one child is a girl," the gender of the other child is no longer independent. If you learn that "the older child is a girl," then you have definite knowledge about the older child, but you know nothing about the younger. The younger child's gender is again independent.

There are 3 points, then, that relate to color rendering:
1. Even a tiny dose of logic can create an element of surprise or mystery.
2. When you follow through the logical answer, it takes the mystery out of the problem. This is characteristic of analyzing something logically. When you list the cases, the mystery of the 2-child problems falls away.
3. When some of the mystery is gone out of color rendering, you may find that it is an important subject, more important than you thought.

That's it really. Many discussions of color rendering convey a single fact, that the light source "somehow" affects what you see. The inner workings of this "somehow" are not explained; the discussion is cut short. In my presentation, I move right into the mysterious inner workings. The way I do this is to bring many tidbits of fact into the discussion. More facts offer more chances for something to seem temporarily mysterious.

>> proceed to another similar puzzle.

 web site designed by Nick Worthey
 More Puzzle Pages
 "Child walks into the room," another interesting version of the boy/girl puzzle (a page on this site). Ask Dr. Math: boy or girl? Marilyn is Wrong! www.mathpuzzle.com
 Basic Facts, New Ideas, etc.
 Read a discussion of Amplitude for Color Matching, and see a colorized 3D graph of the spectrum locus graphed in the orthonormal color space Seek some basic facts? Color Rendering Basic Facts 30 New Ideas from the two color rendering articles Who is Jim Worthey? Read a short biography Jim's Past Publications? See list of articles on color, lighting, etc. Read a version of Richard Feynman's talk on cargo cult science
 Items of Interest
 Medimmune Flumist Who is Nick Worthey? My son, Nick J. Worthey, is an illustrator and graphic designer. You may enjoy his web page, http://www.nickworthey.com. I most enjoy Nick's black and white cartoons.
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