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Gerver Algebra 1, p. 61-62

PT: Fundamental Counting Principle

RW: Phone numbers 

If the first digit of a telephone number is not 0 or 1, what is the probability that on the first try, you will correctly dial the first three digits of a friend’s number if you know the third digit is 8?


The Mathematics Teacher, Vol. 92, No. 9, Dec 1999, p. 768-775

M: Availability

PT: Fundamental Counting Principle

RW: Attribute Game/Logical Reasoning

THE GAME: Twelve cards are placed face up on the table.  Each player looks for a "set" of three cards.  When a player finds a set, she puts it in her own pile, then three new cards are placed on the table to bring the total back to twelve.  The game continues until all cards are dealt and no more sets can be found.  If at any time during the game no sets can be found, three more cards are added until a set is found.  The player with the most sets at the end of the game wins.

CARDS:  Each card can be identified by four attributes, each of which has three values: number - 1, 2, or 3; color - red, green or blue; symbol - diamond, oval, or square; and shading - open, striped, or solid.  The deck is made up of one card of each type.

SETS:  Three cards make a set if, for each attribute, the values on the cards are either all the same or all different.

QUESTIONS:

1)   How many cards are in the deck?

2)   How many sets, including overlapping ones, are possible?

3)   Which types of sets are you most likely to find?

4)   If twelve randomly selected cards do not contain a set and three additional cards are added, what is the probability that a set will be present?

5)   What is the probability of having two disjoint sets among twelve randomly selected cards?


Key to Problem Bank:

M: Misconception PT: Probability Topic RW: Real World Topic