Calculating Probability As A Ratio

Calculating Probability As A Ratio

Who Is More Likely to Win?

Opening

Who Is More Likely to Win?

Watch the Wheel video.

  • Who do you think is more likely to win? How do you know?
  • Think about the situation, and then discuss your ideas with a partner.

VIDEO: Wheel

About Probability

Opening

About Probability

Discuss the following with your classmates.

In everyday life, people often think about whether or not something might happen in the future. Many decisions are based on the chance or probability that a particular event may or may not occur.

Probability involves the study of events whose results are affected by chance. The probability of an event is expressed as a ratio that can be used to predict the likelihood of an event occurring. Probability ratios are values ranging from 0 to 1. Probability ratios may be represented as fractions, decimals, or percentages. If an event has a probability equal to 0, then it is impossible. If an event has a probability equal to 1, then it is certain.

The theoretical probability of a particular event A is the ratio of the number of ways that A can occur to the number of all possible outcomes.

This is represented by the probability formula:

P(A) = an

where

  • a is the number of ways that an event can occur
  • n is the total possible outcomes

Probability is a number between 0 and 1 used to quantify likelihood for processes that have uncertain outcomes (such as tossing a coin, selecting a person at random from a group of people, or tossing a ball at a target).

 

Math Mission

Opening

Find the probability of events.

Assign Probabilities

Work Time

Assign Probabilities

The Assigning Probabilities handout shows a likelihood line that is similar to the one you used in the last lesson.

  • How should the marks for Imposssible, Certain, and Equally Likely as Unlikely be labeled?
  • On the likelihood line, assign a probability from 0 to 1 for these events. Mark each of these events on the line.
    • It will rain tomorrow.
    • You will send a text sometime today.
    • Out of all the students at your school, you will be chosen at random to win a prize.

HANDOUT: Assigning Probabilities

Probability of an Event

Work Time

Probability of an Event

  • What is the probability of this event: rolling a 3 on a number cube that has the numbers 1−6 on it?

Prepare a Presentation

Work Time

Prepare a Presentation

Prepare a presentation that summarizes how to express the probability of an event as a ratio.

Challenge Problem

  • What is the probability that your house will be struck by lightning this year?
  • How could you calculate the probability?

Make Connections

Performance Task

Ways of Thinking: Make Connections

Take notes about calculating probabilities.

Hint:

As your classmates present, ask questions such as:

  • Was it harder to assign probability to some events than others?
  • For which events do you know the total number of outcomes?
  • How did you decide the probability of each event on the line?

Calculate Probabilities

Work Time

Apply the Learning: Calculate Probabilities

  • What is the theoretical probability of the following events?
    • Having a spinner land on red on a 4-part spinner with equal-sized, different-colored sections
    • Drawing a diamond from a regular 52-card deck of playing cards
    • Flipping a coin and having it land on heads
    • Drawing a blue marble from a bag with 6 red marbles, 4 blue marbles, and 2 green marbles
  • For each of the events previously listed, how many times do you think the event would occur if you repeated the experiment 120 times?

Theoretical Probability

Formative Assessment

Summary of the Math: Theoretical Probability

Write a summary about theoretical probability.

Hint:

Check your summary:

  • Do you define probability ?
  • Do you describe the ways that probability can be expressed?
  • Do you explain how to calculate the theoretical probability of an event occurring?

Reflect on Your Work

Work Time

Reflection: Reflect on Your Work

Write a reflection about the ideas discussed in class today. Use the sentence starter below if you find it to be helpful.

What I don't understand about probability is...