Probability Puzzles


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 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 inking 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.


When you roll the die, you are playing with probability. With each roll, you are just as likely to get I 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 cache 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 said “Now everyone will know that this car belongs to me!” What was the man’s name?

Even and Odd-Explained

What’s going on? Why does Player E keep winning? There are two possible explanations:

1. If Player E always shows either two or four fingers, the answer will always be even regardless of the number of fingers Player O shows. Player E will win every time.

2. If Player Eis totally honest and shows fingers randomly, then it is the same as using the spinner. Player E will win most of the time. To see why, fill in this multiplication table and circle all the even numbers. Wow!

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