This morning a box of fun-sized M&M packages got delivered to our house (thanks to my mother-in-law aka Grandma). Although this seems like a thoughtful gesture, its a major problem. Why? You might ask? Easy. I have absolutely no will power when it comes to M&M’s, so much so, that a package of M&M’s may have been opened at breakfast this morning. And a package may have also been opened for my 7 year-old. And my 5 year-old. And my 2 year-old. (Don’t be impressed with my husband, the only reason he didn’t open a package is because be was already at work!)
Chocolate in the morning. Everyone should be in a good mood, right? Even better is chocolate covered in brightly-colored candy coating. Unless, of course, that candy coating happens to lay the groundwork for a fight between two pint-sized humans.
“Mom! Jack’s package of M&M’s has all the colors and mine only has two! That’s not fair! Tell him that’s not fair!’
Hmmm, I’m not sure that “not fair” is the phrase that should be used to describe this particular incident. How about “Mom! That’s not likely!”
I know, I know “not likely” is not nearly as moving as “not fair,” but this is a blog about mathematics after all. Fairness is not something that I can speak to in this context, but likely, now that’s something we can talk about!
Here’s what I want you to do. And you have to promise to not cheat. (Promise). Buy a few bags of M&M’s this weekend. As many as you see fit and go ahead and try to determine how “likely” it is that someone will get all the colors of the M&M’s in one fun sized bag. Also, see if you can’t figure out if M&M Mars makes equal numbers of red, orange, yellow, green, blue, and brown M&Ms.
Remember, you already promised you wouldn’t cheat. So I’m trusting you not to just Google this as soon as you’re done here. Besides, you’d get to eat the project when you’re done. If you just Google it, there won’t be anything good to eat.
I’m going to answer this question too. And I’ll show you how I went about answering it . . . next week. In the meantime, send me your methods. Let’s see what we can come up with!