Brain Benders


You might be surprised to know that probability is a relatively new area of math. Probability began

to be studied in the mid-1600s. That may seem like a long time ago, but remember that people have been doing geometry for thousands of years.

Probability is involved any time we do something where we can’t know in advance what is going to happen. When we toss a coin in the air, we know it is going to come back down. However, we don’t know if it will land as heads or tails. That is probability.

Probability: The chances of something happening–actually, the ratio of the number of times it could happen compared to the number of possible things that could happen. For example, when you throw dice, you have 1/6 chances of getting each particular number Probability Scrabble Can you guess how many other words you could make by using any of the eleven letters in the word PROBABILITY? Do you think you could make fifty words, or is the number closer to twenty?

There is no way to know except by sitting down with paper and pencil and making a list.

For each word, you can use each letter as many times as it appears in PROBABILITY. For example, you could spell BABY because there are two Bs, but you can’t spell ROOT, because there is only one o

A Coin Toss

The probability of getting a head or a tail in any coin toss is 1 heads and tails. Do a simulated coin-toss experiment at! java/progsinnotes/Coin Toss.html. First, try 25 tosses, then 100, and then 500. When we tried it, we got 10/15, 50/50, and 251/249.


Then you roll the die, you are playing with probability. With each roll, you are just as likely to get as you are 2, 3, 4, 5, or 6. That means that you have one in six chances to get any number. And each time you throw the die, the probability of getting a particular number remains the same.

This is a game for two players. To play, you will need the following: • Five pennies and five nickels (or two sets of other markers) • A pair of dice • Paper and pencil for keeping score Players should each have five markers, which are prisoners. Player 1 places his or her five prisoners in each cell of the top row. Player 2 places prisoners in the bottom row. Players take turns rolling the dice and subtracting the smaller number from the larger. If the difference matches a cell number, the prisoner kept in that cell goes free (is taken off the board). Whoever frees all the prisoners first, wins!

Who Owns That Car?

A man came into the motor vehicle department to register his new car. He requested a very special license plate with the numbers 337 31770. While signing the paperwork, the mysterious man sad, “Now everyone will know that this car belongs to me!” What was the man’s name?

Unlike the Prisoners Game, this one offers equal chances of winning to all the players, and you can have as many as six people join the game. Here is what you will need to play:

  • each player
  • Pair of dice

You also need to make a game card for each player.

To do that, draw a five squares-by-five-squares grid you can use a ruler to make the lines straight, but it doesn’t matter it they’re wobbly.

Then, have one player read the following list of numbers:

1, 36, 9, 24, 18, 8, 6, 15, 30, 25. 10. 24. 18, 6, 3, 12, 2, 4, 12, 16, 9, 12, 16, 9, 12, 20, 6, 10

As each number is called out, each player should write it down in any one of the squares in the grid, until all the spaces are filled. Some numbers will appear twice.

Once you are done, the game can begin. Players take turn rolling the two dice, multiplying the two results, and then covering one number on the grid. The first one to cover five squares in a row (in any direction) is the winner.

Even and Odd

Here is a game that uses a principle similar to the Prisoners Game and Let’er Roll. To play, you will need two players: Player E (even) and Player 0 (odd), plus the following:

• Piece of paper • Pencil • Paper clip

On the count of three, both players show each other one to live fingers on one hand, Multiply the number of fingers showing on one player’s hand by the number of fingers showing on the other player’s hand. If the product is even Player E wins. If the product is even, Player O wins. Keep a tally for twenty rounds. Which player wins the most rounds?

You should have noticed that Player Ewon many more games than Player O. Will Player E still win if both players use a spinner instead of their fingers? Try it. Use a pencil to hold a paper clip at the conter of the spinner. Flick the paper clip around the spinner. Keep a tally for twenty rounds. Now, which player won the most games?

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