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## #1389. Predicting With Playing Cards

Mathematics, level: Middle
Posted Sat Nov 6 05:00:49 PST 1999 by Bruce Lemoine (Brucel@netaxis.com).
New Canaan Country School, New Canaan, CT USA
Materials Required: Playing cards;
Activity Time: 45 minues or longer
Concepts Taught: Probability; Fractions & Percentages

Begin by creating a list that contains all of the cards in the deck. Here is an example of what the beginning of that list would look like.

A A A A
K K K K
Q Q Q Q

Give the list to the students who will use it to check off cards as they are dealt from the deck. Now, begin by dealing the first two cards, showing them and spliting them as shown:

5 J

Now students have to predict what is the chance that the next card dealt will come between a five and a Jack. The denonminator is 50 since there are 50 chances left in the deck. The numerator is 20 since the winning cards are 6, 7, 8, 9, and 10 AND there are four of each left in the deck. The chances of winning this round are 20/50 or 40%.

As the game progresses, the numbers become more difficult to manage, so equiping students with a calculator is a good idea, but only if they have already learned how to convert fractions to percentages.

Here is how a quiz might look using the logic of this game.

The game is acey-ducey -- two cards are played in a hand, and you have to estimate your chances of drawing a 3rd card that will fall between the two.

1.There are 52 cards in the deck. The first two cards played are a 3 and a 10. Expressed as a percentage, what are your chances of winning?

2.The next card dealt is a 5. You win - congrats! Time for the next hand, and the cards played are a king and a 5. What are your chances of winning?

3.The middle card played is a 10, and you win again! The game continues with a 3 and a 5 played. What is the likelihood you will loose if you make a wager this