 # Probability (Sample Space)

Related Topics:
Common Core for Mathematics
More Math Lessons for Grade 7

Videos, examples, solutions, and lessons to help Grade 7 students learn how to find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

A. Understand that, just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

B. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

C. Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Common Core: 7.SP.8

Suggested Learning Targets

• I can explain that the fraction of outcomes in probability of a compound event is similar to the probability of a simple event.
• I can use tree diagrams, frequency tables, and organized lists to determine the probability of a compound event.
• I can identify the outcomes in a sample space.
• I can represent probability outcomes as fractions, decimals, or percents.
• I can design a simulation to estimate the probability of a compound event.
• I can see a simulation to estimate the probability of a compound event.

### Organized Lists

Coin Flipping Example - Using Organized List
Example: Find the probability of getting exactly two heads when flipping three coins. Compound events using organized lists
Example 1:
Sara is taking pictures of Christina, Micheal and Joseph. She asks them "How many different ways could you three stand in line?"
Example 2:
Today is the ice-cream party. Each person will get a two-scoop cone. They can choose from vanilla, chocolate or strawberry ice cream. A person can have 2 scoops of the same kind of ice cream. Also, a chocolate scoop on top of a vanilla scoop is the same as a vanilla scoop on top of chocolate. How many different 2-scoop cones can be made?

### Tables

Probability of More Complex Outcome - Using a Table
Example:
Find the probability of rolling doubles on two six-sided dice numbered from 1 to 6.
Probability of 2 events. Using sample space diagrams (tables)
Example:
1) What is the probability that I flip a head and roll an even number?
2) If you roll two dice, what is the probability of getting a sum greater than 8?

### Tree Diagrams

7.SP.8.b - List Possible Outcomes for Compound Events
If you've ever been at a restaurant and seen choices for an appetizer, main dish and dessert, have you ever wondered what could the outcomes be if you had to pick one of each from the choices you had? This video shows you how to list the possible outcomes of compound events. This video addresses the modeling of how to find the possible outcomes using tree diagrams, as called for in Common Core math standard 7.SP.8.b.
Example 1:
Elise is planning the menu for a dinner party. She wants to serve one main dish and one salad. For the main dish, she can make vegetable skewers, pizza, pasta, or chicken. Elise knows how to make potato salad or fruit salad. Make a tree diagram and list the outcomes below.
Example 2:
Pamela is planning a vacation. For each place, she can get there by taking a car or a bus. She can go to a city, a river, the ocean, the mountains and one location. What are the different combinations that Pamela can choose from? Probability - Tree Diagrams 1
How to use a tree diagram to calculate combined probabilities of two independent events.
Example:
Jenny has a bag with 7 blue sweets and 3 red sweets. She picks a sweet at random from the bag, replaces it and picks again at random. Draw a tree diagram to represent this situation and use it to calculate the probabilities that she picks
a) 2 red sweets
b) no red sweets
c) at least 1 blue sweet
d) 1 sweet of each color Probability Tree Diagrams 2
Using a probability tree diagram to calculate probabilities of two events which are dependent.
Example:
Jenny has a bag with 7 blue sweets and 3 red sweets. She picks a sweet at random from the bag, but does not replaces it and picks again at random. Draw a tree diagram to represent this situation and use it to calculate the probabilities that she picks
a) 2 red sweets
b) no red sweets
c) at least 1 blue sweet
d) 1 sweet of each color

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