Candy Math Monday is all about demystifying math for the benefit of all, especially our young friends who struggle with math in school or while preparing for the SAT or a similar test. It’s a pain, to be sure, but that’s why we are working with candy – to make math a bit sweeter for you.
Today we will look at probabilities. Notice that the Mike and Ike candies in the photo have about twice as many green pieces than red. Let’s assume that is the exact proportion: two green to one red. If you have a bag of these you are sharing with a friend and you randomly pick one out, what is the probability that it will be a red one?
Break it down
First, what is probability? It is a term used quite a bit, so let’s come to an understood agreement. Basically put, probability is the quantifiable likelihood of something happening. In other words, it is the possibility of a particular outcome over the entire set of outcomes. Simple? I thought so.
How it all works
If we have two green candies for each red one, that is a ratio of 2:1. Add those numbers together and you have three candies total (2 green + 1 red = 3), or some multiple of three, assuming you have a big bag of them. One way to think of this is to imagine what you are trying to find (a red one) out of the total in the bag (including green and red).
One out of three of the candies is red, so you have a one-third chance of getting a red one. Simple answer, right? Well, this is an entry-level problem. Let’s kick it up a notch. If you have the same ratio and five red candies, what is the probability of getting two red ones in a row?
The first thing you have to do is calculate how many candies you have. If the ratio is 2:1 (G:R) and you know you have five reds, then you have ten green ones, right? That means your expanded ratio is 10:5.
The Answer
The first part is easy. We already did that. Five red candies, ten green ones means a 5 out of 15 (5/15) or one-third chance.
The second part is tricky. You have already eaten one red one, or maybe shared it with your friend, so how many are left? You have four left. This changes the ratio, so you have to do some more math. Your new ratio is 10:4. The new probability of getting a red one is 4 out of 14. 4/14 can be reduced to 2/7. It’s easier to work with smaller numbers, so let’s go with that.
So now we have the answers to the first and second parts of the problem. Now we have to bring them together. When dealing with probabilities like this, you have to multiply them to get the final answer.
1/3 * 2/7 = 2/21
So you have a 2/21 chance of getting two red candies in a row. Simple? I thought so.
The key to solving complicated math problems is to break them down into manageable, simpler problems. In addition, putting some candy in the mix adds some fun to the process.
