data and probability – Early Math Counts

Probability and the 3 Door Problem

Tue, 16 Oct 2012 11:00:57 +0000

This one isn’t for children, it’s for you. This is a classic probability question that has puzzled game show contestants for years.

Remember the game show “Let’s Make a Deal”? It is back on TV, new host, same idea. People dress up in costumes and hope to get called down to the stage to “Make a Deal”. One of the games you might remember is the 3 Door Problem.

The host tells the contestant that there is a car behind one door and goats behind the other two doors. The contestant then has to choose one of the three doors. Next, the host opens one of the other doors and reveals the goat. Now, there are only two doors. The contestant has chosen one, one is unknown and the other is open with a goat behind it.

The host now asks the contestant if s/he wants to switch doors. Do you think s/he should? Will it increase the chances of winning if the contestant switches?

Most people think that the chances are winning are even, since there are now two doors and it seems that there is a 50/50 chance of choosing the correct door. They would be wrong.

Let’s go back to the beginning. When the contestant first chose his chances were 1/3 or 1 out of 3 chances that the choice is correct. That also means that there was a 2/3 chance that the choice was incorrect.

When the host removes one of the doors as a choice, there remain two doors. However, if the contestant keeps his/her choice the chances of winning are still 1/3 (it hasn’t changed at all).

If the contestant guessed correctly to begin with and changes his/her choice then s/he has 0 chance of winning.

However, if the contestant guessed incorrectly the first time, changing his/her answer increases the probability of winning to 2/3.

If you don’t believe me, set up the game with cups and a ball and keep track of the odds. If you play enough, you will begin to see that this is in fact, true. Amazing, yet true!

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Probability Redux

Tue, 09 Oct 2012 11:00:38 +0000

Chance games are something that people often like all the way through adulthood. Think of Roulette and that big round wheel going round and round until the ball falls on black or red, odd or even. There is a rush of excitement when you think you have predicted correctly. In my house we love watching “The Price is Right” and all of those chance games. Think of Plinko and Roll ‘Em. They are all games based on probability. Even the big wheel that the contestants spin to see if they are going to the Showcase Showdown is really a game of chance.

Using dice, coins, and spinners, we can introduce the concepts of probability to young children fairly easily. You can create a spinner like this one to help children see – in an obvious way – that they can predict which color the spinner will land on. Since the portions are unequal, the children can see that there is a greater likelihood that the spinner will land on red than on blue.

If you use a standard spinner from a game of Twister, it is much, much more difficult to predict what will happen. There is actually an equal chance of landing on yellow, red, green or blue each time that you spin.

The same is true for a 6 -sided die. It may be hard for young children to predict when there are 6 choices.

So, a coin may be the easiest. There are only 2 choices; heads or tails. Each time you flip the coin, there is a 50/50 chance of predicting the outcome correctly.

Try some of these ideas and let us know how they go.

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www.mathathome.org (cont.)

Wed, 18 Jul 2012 11:00:29 +0000

Hopefully, you have now made the connection between this blog and the Early Math Counts website. Some of you may be accessing this blog directly, while others have found it through the website home page. Either way, we are glad you are here.

Today we are going to take a look at the “Increase Your Knowledge” page on the Early Math Counts website. This page and its content was designed for the early childhood professional as well as the early childhood layperson (parent or guardian) who wants to increase their own knowledge about basic math concepts.

If you scroll to the middle of the page you will see seven small images that will link you to short, informative videos. These are about 3-5 minutes each and will either serve as a reminder about math concepts you may have learned many years ago (some of us haven’t been in school for awhile) or may be completely new to you.

The more we deepen our own understandings of math concepts the better we will be able to serve children. As our own knowledge increases so does our confidence in working with specific material.

Click on the “Data and Probability” link and watch the video. What do you think? Did you learn something new or did you dust off some old memories of math concepts long since buried?

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