I'm Bon Crowder and the photos above are both of me - in 1989 and today. I'm a Generation X mom of Generation Z kids.

I began peer tutoring in high school in 1984. MathFour.com is the 2015 version of me helping peers be comfortable in math.

If you're a Gen-X parent, you're in the right place!

# Tag Archives: probability

### Football vs. Furniture – A Tale of Probabilities

We have a local legend, icon and hero here in Houston, where I live. His name is Mattress Mack and he owns a furniture store.

Okay, his real name is Jim McIngvale and his furniture store is a little more than just that. It’s THE furniture store.

He’s built this amazing empire of furniture sales doing crazy, fun and remarkable things.

This past weekend was no different.

### Gambling with Football and Furniture

I got an email on Friday – two days before the AFC and NFC championship football games.

They were running a(nother) bizarre promotion.

Here’s the gist of the rules:

1. Purchase \$5,000 or more of furniture from Gallery Furniture (the name of this iconic furniture store).
2. Have it delivered by 2PM CST Sunday, January 19, 2014 (before the first football game starts).
3. Choose you you think will win both football games.
4. Pick the winner of both games right and you get your money back on your purchase (yep – all \$5000+ dollars you spent).

Sounds crazy, right?

I read the rules four times. It was fact. They were really doing this.

### The Math behind the Madness

I immediately started thinking about the math.

Two games. Two winners. 25% chance of guessing both of them right.

The probability tree looks like this:

So, mathematically, for every \$20,000 in sales, Mattress Mack will give back \$5000. Assuming his profit margin is more than 25%, he’ll still be in the black.

I did some quick research and found that the furniture retail industry has around a 40% profit margin.

I breathed more easily knowing that – at least statistically – Mattress Mack was going to come out fine.

### People Picked – People Won

I read today that 85% of the players won in this crazy game of football vs. furniture.

Which blows the 25% I originally figured out of the water.

It cost Mattress Mack \$600,000.

Yipes!

### Who would play this game?

Doing a little arithmetic, we can see how many people joined in on the game:

\$600,000 was the payout, which means about 600,000/5,000 = 120 people won.

85% of the people who played won, so we can use this equation to model the number of players:

120/x = 85/100, where x is the number of players

Solving for x, we see that about 140 people played.

### Good Idea or Just an Idea?

If he was only playing the numbers, he’d have been okay.

Alas, he forgot to consider what the parimutuel betting folks factor into their games (as well as actuaries). There are favorites in football games. And there are long shots.

Mattress Mack set up the game as if there were equal chances of each team winning. Thus giving him the clear advantage.

But there were not equal chances.

Unfortunately for Mack (and fortunately for 120 people), it wasn’t a “fair” game.

### He’s still our hero!

Mattress Mack is as crazy as he once was. And we still love him.

Especially since his reaction was, “I realized it was a great success because it made a lot of customers happy.”

Can’t deny that!

### 3 Responses to Football vs. Furniture – A Tale of Probabilities

1. Thank you so much for your kind words and support of Gallery Furniture!

We are so excited for all the great customers who won based on our previous Pigskin Promotion where Gallery Furniture is paying out over \$650,000 in refunds to our fantastic customers. We are even more excited about our NEW Big Game Promotion where we will pay out millions more if the team from Seattle wins.

If you ever relocate to Houston, make sure to come visit us! Gallery Furniture delivers same day and has the highest quality furniture and accessories in Houston! When you shop with Gallery Furniture, YOU CANNOT LOSE!

• Bon says:

Hey y’all! I’m always glad to support a local business and hero.

I’m excited to hear about your SuperBowl promo – I’ll keep my eyes peels in my inbox!

• Thanks Bon, as always we truly appreciate your support! We’re all thrilled for our amazing customers who won the Previous Pigskin Promotion. Our NEW Big Game Promotion sure is exciting with The Big Game right being around the corner! As our owner and fearless leader Mack said, What’s good for Gallery Furniture customers is good for Gallery Furniture and good for Houston! Gallery Furniture is a touchdown for every customer, every time! http://bit.ly/BigGamePromo

### Blog Giveaways – How People Lose

Did you know that by sharing a blog giveaway, you’re REDUCING your chances to win!? Sounds nuts – but there’s math behind it! Continue Reading

### 3 Responses to Blog Giveaways – How People Lose

1. Karleen Mauldin says:

Bon, I’m in no way a “math” person, but yes, I figured that out a long time ago!! I’m like you — why do I want *more* people to enter since that will *reduce* my chances of winning?! Ha! Plus, I don’t like my FB newsfeed clogged with “so-n-so entered a contest–you can too!” so I really don’t want to do that to others. So even trying to be nice & considerate will reduce the number of times you are entered in a contest.

2. Bad Bon. I love the article, now I don’t know what to do. I host giveaways myself so I better keep sharing. Now I will think of you every time I enter (and share) a giveaway and the math behind it!

3. T. says:

Evil, evil social media…

### Probability Tree Diagrams as Puzzles!

Probability tree diagrams are a tool to help students find probabilities. But they can also be a puzzle. Learn how and get the FREE DOWNLOAD here! Continue Reading

### 2 Responses to Probability Tree Diagrams as Puzzles!

1. Alice Petillo says:

Is there a reason why the second example hasn’t been corrected/updated?

• Bon says:

Yes, Alice, there are a few.

1. I’m crazy busy with lots of other things.
2. This is a minor error that only one person in 2.5 years has noticed.
3. The important content of the piece is error-free.
4. I have a list of things to do on the blog that has about 130 things on it.
5. It’s nice to let others discover the error too.

All things taken together, it’s just not even on the list to get fixed.

However, I appreciate you commenting about it so that others will know that when they find the error, they aren’t crazy.

### The Math Behind the Monty Hall Problem

As promised, here’s the “hard way” to understand the Monty Hall Problem. A little math involved, but also the Back to the Future Time Machine! Continue Reading

### One Response to The Math Behind the Monty Hall Problem

1. Jim Briggs says:

This is the first explanation I have heard or read that enabled me to understand why you should switch. Great job! It still seems counterintuitive, but at least now I get it.

### The Monty Hall Problem Explained – The Easy Way

There are a couple of ways to explain the Monty Hall Problem – the easy way and the hard way. I have to make cheesy potatoes, so the hard way comes tomorrow… Continue Reading

### 2 Responses to The Monty Hall Problem Explained – The Easy Way

1. Dave says:

I don’t understand. You only have to pick from two doors that you don’t know what’s behind, so the chance is 50/50.

• Bon says:

That’s the point, Dave. It’s kinda not that simple. Creepy and weird, though, for sure!

Thanks for stopping by.

### Math Crafts: Probability Earrings

Want to get your homeschool teenager to do probability? Try heading to the bead shop first. This video shows probability in action with a beautiful end result. Continue Reading

### In How Many Ways Can You Solve the Thiagi Circles Jolt?

A fun puzzle from world famous Thiagi – and the number of different ways to solve it! Continue Reading

### How to Calculate Permutations and Combinations

The two previous posts showed how to tell the difference between permutations and combinations and how to work with factorials. Now you’re ready to do some calculations! Continue Reading

### 2 Responses to How to Calculate Permutations and Combinations

1. maria says:

hi
In the question: “in how many ways can 4people be seated in a row of 12 chairs?”
how can i tell of its a permutation or combination?

• Bon says:

The real question turns out to be one of these:

You have 12 chairs in a row. How many ways can you pick four of them to have four different people sit in? (permutation)
OR
You have 12 chairs in a row. How many ways can you pick four of them to have people sit in? (combination)

Explanation:

It sometimes helps if you think about an example. Say your four different people are Adam, Betty, Carl and Diane. Now consider a few possible ways they can sit in that 12-chair row.

ABCDxxxxxxxx
BACDxxxxxxxx
xABCDxxxxxxx
xBACDxxxxxxx
AxBCDxxxxxxx
BxACDxxxxxxx

These are only a few. But look at the first two. Those look different. And indeed Betty might really be into Carl, so she’d definitely argue that they’re different. If you consider them different, then it is permutation.

Now supposed we don’t care that the people are different. The question then is, “How many ways can you pick four chairs to have people sit in?” The above examples now look like this:

PPPPxxxxxxxx
PPPPxxxxxxxx
xPPPPxxxxxxx
xPPPPxxxxxxx
PxPPPxxxxxxx
PxPPPxxxxxxx

So now it’s clear that this is a combination – because the chairs are merely being occupied by some human (no preference, order or importance as to whom actually gets their heiney into the seat).

So really, the question is – how do you interpret the original question?

### Permutations and Combinations – How to Tell the Difference

Have you ever been told that “In permutations, order matters”? There are lots of permutation problems where there’s no ordering whatsoever. So how can you tell?!? Here’s how. Continue Reading

### 19 Responses to Permutations and Combinations – How to Tell the Difference

1. evan says:

umm thx sorta????

• Bon says:

Evan, what’s the “sorta” about? Are you still confused? How can I help?

2. Mercedes says:

I think it’s a good idea, I’ll try it next time I’ll explain that, at the end of the semester.

3. claire says:

Thanks. I was in the “order matters” camp.

• Bon says:

No problem, Claire! I hope you’re in the “all is good with these” camp now.

4. Allen Arnold says:

Bon – It’s a much better idea than the “order matters” thing. I use this with my students and it works. There are also problems on the SAT where this will be useful. It was something like: How many ways are there to choose a President, Vice-President, and a Secretary from five people. No order there, but it’s a permutation problem! A slightly more complicated way to do this is to first calculate how many ways to select the three people (a combination), then ask how many ways can you assign the three chosen people to fill the three offices. Then you multiply the two answers. However, your way is much easier. Thanks for the tip.

5. Bon says:

Thanks so much, Allen. It is frustrating to students to try to figure out if where there is “order” when there is, technically, none.

When I create my own questions, I always make sure to match the permutation version with the combination version. On a recent test, I asked students to determine which to use between these:

A. From five paintings, you need to choose three for your new office.

B. From five paintings, you need to choose one for the lobby, one for the bathroom, and one for the conference room.

I think when students see them back to back like this, it’s much more helpful to learn the differences.

Thanks for stopping by!

6. Mike says:

I’m still confused. I have some math problems, and book has this under the permutation section, but I can’t see why.
18. Fifteen students ask to visit the admissions representative from State University. Each visit includes one student. In how many ways can ten
time slots be assigned?
19. How many different nine-player batting orders can be chosen from a baseball squad of 16?
20. The prom committee has four sites available for the banquet and three sites for
the dance. How many arrangements are possible for the banquet and dance?

• Bon says:

Mike – notice the time slots are all different. When you have each chosen thing (the students) doing different things (going at different times), then it’s a permutation.

For #19 – when you bat makes a difference. So if you are first at bat or third, that’s different. Different things for each chosen player to do means permutation.

And #20 – This one goes back to the multiplication principal. 4 x 3 would give you the various arrangements. If you notice, textbooks often throw in something from previous sections to help you make the connections that different methods will give you same results.

7. Amelia Weller says:

Wow– this makes so much more sense than the “order matters” deal. Wish my finite professor had taught us this way!

• Bon says:

Thanks for your kind words, Amelia!

8. Dan says:

I have to let my little nephew know about this site. You are better at explaining things than some teachers.

• Bon says:

That’s sweet of you to say, Dan.

9. Carly says:

Thank you very much Bon! This made me understand the difference much better, instead of just using the textbooks. I will suggest these videos to my friends and teachers !!

• Bon says:

10. erika says:

So everytime the problem say something different it permutation? ? Wat would this be
If andy has 7 shirts 6 pants and 8 ties how many diferent outfits can he make wiTh pants shirts and ties.
And
There are 6 puppies born but the mother always feeds only 4 puppies at a time. How many differemt groups can she feed at one time?
And are there any special words to look for in these word problems

11. Kevin says:

No wonder I could never figure out what I was being taught about these two. That whole order thing just confused the heck out of me. Now I get it! Thanks.

• Bon says:

I’m so glad it helped, Kevin!

12. Calvin says:

Dude ur awesome I actually think I might do well on my Algebra 2 EOC that I have to take in about 45 minutes

### How to Pronounce n! and How to Use Factorials

You may have seen n! – and I don’t mean to scream the 14th letter of the alphabet at you. So what the heck are factorials and why do you ever need to learn them? (Guess what – the answer is in this post!) Continue Reading

### 2 Responses to How to Pronounce n! and How to Use Factorials

1. Kelly says:

Can I just say that you are a brilliant angel of math! I have such a hard time with it and you explain things in such easy examples that I finally figured these factorials out.

Thank you, thank you, thank you!

• Bon says:

Kelly, you’re so kind! And I’m very glad to be able to help.

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