6th Grade Math Textbook, Fundamentals

Lesson 12-5 for exercise sets. &KDSWHU 

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Find the odds in favor of and the odds against each outcome for rolling a
fair 1–6 number cube. Write each pair of odds in simplest form.

1.an odd number 2.a composite number 3.a number divisible by 2

4.Jim and Dan play a game. If a coin lands on heads, Jim wins. If a coin

lands on tails, Dan loses and Jim wins. Are both players equally likely

to win the game? Explain.

5.Discuss and Write Write a formula for converting odds to theoretical

probability. Explain how you found your formula. (Hint:Think about the

number of favorable outcomes, the number of unfavorable outcomes, and

the number of possible outcomes in the sample space, and how they relate.)

You can use odds to determine if a game is fair. A game is said

to be if the number of favorable outcomes is equal to the number

of unfavorable outcomes. Players are equally likely to win the game.

The odds of the events in fair games are 1 : 1.

Odds that take the form 1 : 1 in simplest

form are called evenodds, or the same odds.

This means that the odds in favor of an event

happening are the same as the odds against

the event happening.

• Frank has two coins. On one coin, he will tape a piece of blue paper to
  both sides. On the other coin, he will tape a piece of blue paper to one
  side and a piece of red paper to the other side.
  Frank proposes the following game to Lena.
  Frank tosses both coins. If both sides are the same color, Frank wins a point.
  If the sides are different colors, Lena wins a point. Lena then tosses the
  coins with the same rules. Play proceeds until Frank and Lena have each
  tossed the coins 15 times. The player with the most points is the winner.
  Is this an example of a fair game?
  Make a table to see all possible outcomes of the game.
  Let B blue.
  Let R red.
  From the table, you can see that there are 4 outcomes
  in the sample space.
  Two outcomes (BB, BB) favor Frank, and
  two outcomes (RB, RB) favor Lena.
  The odds in favorof Lena winning are 2 : 2 or 1 : 1.
  Similarly, the odds againstLena winning are 1 : 1.
  So the game is fair because it has the same odds.

fair

BB

BBBBB

RRB RB

Coin 2

Coin

1

Think

Odds of 1 : 1 mean that of 2 possible outcomes,

1 is favorable and 1 is not favorable.

P(E)  means that 1 of 2 of the possible

outcomes are favorable.

So odds of 1 : 1 is the same as a probability of.^12

1

2