## Chances Are . . .

Mathematics, Data Analysis and Probability

### Objective

Students will learn how to determine the probability that an event will occur.

### Directions

Go over the following facts and reminders with the students. Use coins and dice to illustrate the different probabilities.

Facts and Reminders
Whether an event is likely to happen can be expressed by a number. This number expresses the probability or likelihood that a particular event will occur. You can determine the probability that an event will occur by counting all of the possible outcomes.
Flipping One Coin
When you flip a coin, only two possible outcomes can result. You have one chance in two of flipping heads (or tails). If you flip the coin 50 times, you have 1/2 x 50 or 25 likely flips with heads showing. When you actually flip the coin, however, the results may be quite different. The more times you flip the coin, however, the greater the likelihood that you will end up with exactly half the coin flips as heads.
Flipping Two Coins
Listed below are the possible outcomes when you flip two coins. (H = heads, T = tails, 1 = first coin, and 2 = second coin)
H1 H2
H1 T2
T1 T2
T1 H2

You have one chance in four of flipping two heads. You have one chance in four of flipping two tails. You have two chances in four (or one chance in two) of flipping one head and one tail.
Flipping Three Coins
Listed below are the possible outcomes when you flip three coins. (H = heads, T = tails, 1 = first coin, 2 = second coin, and 3 = third coin)
H1 H2 H3
H1 H2 T3
H1 T2 H3
H1 T2 T3
T1 H2 H3
T1 H2 T3
T1 T2 H3
T1 T2 T3

You have one chance in eight of flipping three heads. You have one chance in eight of flipping three tails. You have three chances in eight of flipping two heads. You have three chances in eight of flipping two tails.
Rolling One Die
You have one chance in six of rolling any particular number with one die.
Have students complete any or all of the three activity sheets to practice figuring out probabilities.

### Resources

• pencil
• coins
• dice
• activity sheets