# Probability

## Objective

Determine the probability of events.

## Common Core Standards

### Core Standards

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• 7.SP.C.7.A — Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

• 7.SP.C.7.B — Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

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• 5.NF.A.2

## Criteria for Success

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1. Understand the probability of an event can be represented as a fraction, where the numerator is the number of desired events and the denominator is the number of total events.
2. Find the probability of “or” and “not” events.
3. Interpret information from tables to determine probabilities of events.
4. Determine the impact of a changing sample space on probabilities of events.

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## Anchor Problems

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### Problem 1

A board game has a spinner with four different options of how a player can move: move forward 1 space, move forward 2 spaces, move backward 1 space, or lose a turn. The probabilities of spinning each option are shown below.

 Spin Move forward 1 space Move forward 2 spaces Move backward 1 space Lose a turn Probability ${{1\over2}}$ ${{{{1\over12}}}}$ ${{1\over3}}$ ${{{{1\over12}}}}$
1. What is the probability of a player moving forward on his or her turn?
2. What is the probability of a player either moving backward or losing a turn?

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### Problem 2

Students in the sixth and seventh grade at your school are going on a field trip to the Science Museum. If a student returns his or her permission slip by May 1, then he or she is entered into a raffle to win a \$25 gift card to the museum gift store. The table below shows the number of students in each grade and from each homeroom who returned their permission slip by May 1.

 Homeroom 1 Homeroom 2 Homeroom 3 6th Grade 7 6 8 7th Grade 10 9 10

One student will win the raffle by random selection. What is the probability that

1. the winner is a seventh grader?
2. the winner is a seventh grader from Homeroom 2?
3. the winner is from Homeroom 3?
4. the winner is not from Homeroom 1?

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### Problem 3

A bag contains different colored jelly beans. In the bag, there are 5 red jelly beans, 3 blue jelly beans, 2 green jelly beans, and 2 yellow jelly beans.

1. What is the probability of picking a blue jelly bean from the bag?
2. Some orange jelly beans are added to the bag. After adding these new jelly beans, the probability of picking a yellow jelly bean changes to ${{1\over8}}$. How many orange jelly beans were added?

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## Problem Set

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## Target Task

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Lucia’s full name is Lucia Andrea Sanchez. For her birthday, her aunt makes cupcakes and writes one letter from Lucia’s full name on each cupcake.

If a cupcake is randomly chosen, what is the probability that:

a.   the cupcake has the letter A written on it?

b.   the cupcake does not have the letter C written on it?

c.   the cupcake has a vowel written on it?

#### Mastery Response

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