# Probability

## Objective

Determine the probability of compound events.

## Common Core Standards

### Core Standards

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• 7.SP.C.8 — Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

## Criteria for Success

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1. Determine the sample space for a compound event and use lists, tables, or tree diagrams as needed to organize the sample space.
2. Determine the probability of compound events.

## Tips for Teachers

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### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Problem 1 (benefits from worked example) and Anchor Problem 3 (can be done independently). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

## Anchor Problems

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### Problem 1

A fair six-sided die is rolled twice. What is the theoretical probability that the first number that comes up is greater than or equal to the second number?

#### References

Illustrative Mathematics Rolling Twice

Rolling Twice, accessed on June 14, 2017, 2:49 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

### Problem 2

Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the theoretical probability that Angie and Carlos are seated opposite each other?

#### References

Illustrative Mathematics Sitting Across from Each Other

Sitting Across from Each Other, accessed on June 14, 2017, 2:40 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

### Problem 3

A standard deck of playing cards includes 52 cards, equally divided among 4 suits: hearts, diamonds, clubs, and spades.

You have two standard decks of cards. You draw a card from the first deck, record the suit, and then draw a card from the second deck and record the suit.

1. What is the probability that you draw a heart and a diamond, in that order?
2. What is the probability that you draw a heart and a diamond, in any order?

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

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Lin plays a game that involves a standard number cube and a spinner with four equal sections numbered 1 through 4. If both the cube and spin result in the same number, Lin gets another turn. Otherwise, play continues with the next player. What is the probability that Lin gets another turn?