Typo in Sklansky Column

Probably several readers have already pointed out this typo, but Sklansky's column in the October 11, 2002 issue of Card Player contains the following: "There are 30 children in your child's class. How many are either boys or redheads? If I tell you that there are 13 girls and four redheads, that doesn't mean the answer is 17...To get the right answer, you would in fact have to subtract the number of redheaded boys from 17." Clearly, the "13 girls" should be "13 boys." Obvious typos such as this one will not trouble the reader with a smattering of knowledge about probability. The totally unsophisticated reader, asked the question "See Why?", will drive himself crazy in a doomed attempt to see why. A published correction would be useful.

[Mike Haven]

no

there are 17 boys (13 girls)

there may be, say, 2 redheaded boys, so of the 4 redheads 2 are girls

so there are 19 boys or redheads (in this case)

or, take 2 redheaded boys from 17 boys = 15, and add the 4 redheads = 19 boys or redheads

[ronniejames]

You need to read more carefully. You'll notice that you consider that the answer might be 19. Sklansky writes: "To get the right answer, you would in fact have to subtract the number of redheaded boys from 17. See why?" There are two possible typos in the column. If the published "13 girls" was intended to be '13 boys', then everything else is correct. If, as you suggest, we are to subtract the 13 girls from a total of 30 children, giving us 17 boys, then the two places where the number 17 appears should read, 21. I do not, even for a moment, entertain the possibility that Sklansky gave the wrong answer. It's too simple and he's far too competent.

[Mike Haven]

i didn't see his article

i gave an example to show that his instructions were correct

his instructions are correct:

"There are 30 children in your child's class. How many are either boys or redheads? If I tell you that there are 13 girls and four redheads, that doesn't mean the answer is 17...To get the right answer, you would in fact have to subtract the number of redheaded boys from 17."

if i tell you there are 13 girls in a class of 30 there are 17 boys

if i tell you there are 4 redheads they may be boys or girls

if there are, say, two redheaded boys then you have to subtract this number from the 17 boys = 15

then add the 4 redheads = 15 + 4 = 19

otherwise you are double-counting the redheaded boys

[ronniejames]

Mike, read Sklansky's words: "To get the right answer, you would in fact have to subtract the number of redheaded boys from 17." Now, you can't subtract any number of redheads from 17 that will yield an answer of 19! If we agree that there are 17 boys and 4 redheads, then the number of children who are either boys or redheads can be 21 (if all the redheads are girls), 20, 19, 18, or 17 (if all the redheads are boys). So, if Sklansky wants us to subtract the number of redheads from 17, something is obviously wrong: he should be asking us to subtract from 21. I suggest that he intended to write, 13 BOYS and 4 redheads, and somehow it came out in print as 13 GIRLS.

[Mike Haven]

"To GET the right answer ..."

the calculations don't STOP at "... you would in fact have to subtract the number of redheaded boys from 17"

they INCLUDE that process

to make your ham and eggs you have to get a chicken first - well - maybe not - but you take the point?

[ronniejames]

I'm afraid I have to throw in the towel. I just don't understand what you're driving at. It really isn't all that complicated. Really.

[BruceZ]

There are 30 children in your child's class. How many are either boys or redheads? If I tell you that there are 13 girls and four redheads, that doesn't mean the answer is 17.

No, why would anyone think it is 17? One might naively think it is 21, since this is 17 boys + 4 readheads. But then you would have to subtract the redheaded boys from 21 not 17. Clearly this is a typo and both bold words above should be boys. Then you subtract redheaded boys from 17 to get the final answer. This is how the demonstration of the inclusion-exclusion principle should be done.

boys OR redheads = boys + readheads - redheaded boys

[Mike Haven]

yep - it's a typo alright - i think it should be corrected to save anyone becoming confused

[happyjaypee]

boys OR redheads = boys + readheads - redheaded boys

Skanlsky explanation would work whit the fellowing equation too:

boys OR redheads = <font color="red"> boys - redheaded boys </font color> + readheads

Is thought process is just in the midlle of the explanation. I agree tought that it is confusing. I reed the post on CP and got a little lost. I Understanded it reading your posts

[BruceZ]

True, but I'm sure it's a typo because of the suggestion that someone might incorrectly think the answer should be 17 (instead of 21). Just changing girls to boys causes everything else to make perfect sense.

but what if one of the children who *isn't* a boy also *isn't* a girl. that happens sometimes, sadly. many corrections are needed to make this column make sense; Sklansky should make them before someone loses a bundle in a high stakes game

[ronniejames]

In my original post, I attempted, in all innocence, to point out a typo in David Sklansky's most recent column. I never considered the possibility that I was instigating a debate---I mean, what is there to debate? Guys: this is not complicated stuff. Let's give it a rest.

[Mike Haven]

lol! /forums/images/icons/grin.gif

we're just funning wid ya ronnie! /forums/images/icons/smirk.gif

[ronniejames]

You guys had me worried. Mike, if you're ever in New York City, I'll buy you a pint of Guinness and introduce you to a fantastic Irish card magician at a pub called Cronin &amp; Phelan's.

[Mike Haven]