Name Class Date 10-1

Name

Class

Date

Probability

Going Deeper

Essential question: How can you describe the likelihood of an event?

CC.7.SP.5

1 EXPLORE

Likelihood of an Event

When a number cube is rolled once, the possible

numbers that could show face up are

.

Each time you roll the cube, a number lands face up. This is called an event. Below is a list of 9 different events.

Work with a partner to order the events from those least likely to happen to the ones that are most likely to happen when you roll the number cube one time.

Use the space next to each event to write any notes that might help you order them.

Rolling a number less than 7

Rolling an 8

Rolling a 1, 2, or 3

Rolling a 5

Rolling a number other than 6

Rolling an even number

Rolling a number greater than 5

Rolling an odd number

Rolling a prime number

The order I wrote the events in is:

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REFLECT 1a. How did you sort the events?

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1b. Are any of the events impossible?

An experiment is an activity involving chance in which results are observed. Each observation of an experiment is a trial, and each result is an outcome. A set of one or more outcomes is an event.

The probability of an event, written P(event), measures the likelihood that the event will occur. Probability is a measure between 0 and 1 as shown on the number line and can be written as a fraction, a decimal, or percent.

If the event is not likely to occur very many times, the probability of the event

is close to 0. Likewise, if an event is likely to occur many times, the event's

probability is closer to 1.

Impossible

As likely as not

Unlikely

Likely

Certain

CC.7.SP.5

2 EXAMPLE

0

1

4

0

0.25

0%

25%

Describing Events

1 2 0.5 50%

3 4 0.75 75%

1

1.0 100%

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. Then, tell whether the probability is 0, close to 0, _12, close to 1, or 1.

A You flip a coin. The coin lands heads up.

B You roll two number cubes and the sum of the numbers is 10.

C A bowl contains 14 red marbles and 3 green marbles. You pick a red marble.

D A spinner has 10 equal sections marked 1 through 10. You spin and land on a number greater than 0.

TRY THIS!

Describe each event as impossible, unlikely, as likely as not, likely, or certain. Tell whether the probability is 0, close to 0, _12, close to 1, or 1.

2a. A hat contains pieces of paper marked 2b. A spinner has 6 equal sections marked

with the numbers 1 through 16. You pick

1 through 6. You spin and land on 0.

an even number.

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REFLECT

2c. The probability of event A is _13. The probability of event B is _14. What can you conclude about the two events?

The complement of an event is the set of all outcomes not included in the event. For example, consider the event that you roll a number cube and get a 3. The complement is the event that you do not roll a 3. The complement is rolling a 1, 2, 4, 5, or 6.

The sum of the probabilities of an event and its complement equals 1.

P(event) + P(complement) = 1

CC.7.SP.5

3 E X A M P L E Using the Complement of an Event

In a standard deck of cards, the probability of choosing a card at random and getting an ace is _113_. What is the probability of not getting an ace?

P(event) + P(complement) =

P(ace) + P(

) = 1

____ + P(

) = 1

P(not getting an ace) = 1 - ____

= ____

TRY THIS!

3a. A jar contains balls marked with the numbers 1 through 8. The probability that you pick a number at random and get a 5 is _18. What is the probability of not picking a 5?

3b. You roll a number cube. The probability that you roll an even number is _12. What is the probability you will roll an

odd number?

REFLECT 3c. Why do the probability of an event and the probability of its complement add up to 1?

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3d. Give an example of a real-world event and its complement.

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PRACTICE

1. In a hat, you have index cards with the numbers 1 through 10 written on them. You pick one card at random. Order the events from least likely to happen to most likely to happen.

You pick a number greater than 0. You pick an even number.

You pick a number that is at least 2. You pick a number that is at most 0.

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain. Then, tell whether the probability is 0, close to 0, _12, close to 1, or 1.

2. randomly picking a green card from a standard deck of playing cards

3. randomly picking a red card from a standard deck of playing cards

4. picking a number less that 15 from a jar with papers labeled from 1 to 12

5. picking a number that is divisible by 5 from a jar with papers labeled from 1 to 12

6. The probability of rolling a 5 on a number cube is _16. What is the probability

of not rolling a 5?

7. The probability that a coin will land heads when flipping a coin is _12. What is

the probability of getting tails?

8. The probability of spinning a 4 on a spinner with 5 equal sections marked 1 through 5 is _15. What is the probability

of not landing on 4?

9. The probability of picking a queen from a standard deck of cards is _113_. What is the probability of not picking

a queen?

10. Describe an event that has a probability of 0% and an event that has a probability of 100%.

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Name

Class

Additional Practice

Date

10-1

Determine whether each event is impossible, unlikely, as likely as not, likely, or certain.

1. rolling an even number on a number cube labeled 1 through 6

____________________

2. picking a card with a vowel on it from a box of cards in which each letter of the alphabet is written on a card

____________________

3. spinning a number greater than 2 on a spinner with 10 equal sections marked 1 through 10

____________________

4. drawing a red marble from a bag of black, blue, and green marbles

____________________

5. flipping a coin and getting heads or tails

____________________

6. rolling a number that is less than three 5 times in a row on a number cube labeled 1 through 6

____________________

Solve.

7. A bag contains 3 green marbles, 7 blue marbles, and 2 black marbles. The probability of randomly picking a green marble is 1 . What is the probability of not picking a green marble? 4

8. A spinner has 8 equal sections labeled 1 through 8. The probability of spinning a number that is greater than or equal to 6 is 3 . What is the probability of spinning a number that 8 is not greater than or not equal to 6?

9. The probability of randomly drawing a red card from a bag that contains red, blue, and green cards is 3 . What is the 10 probability of not drawing a red card?

____________________ ____________________ ____________________

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