Introduction to Probability
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Questions and Answers

What are the learning targets for this lesson on probability?

Recall probability, Identify terminologies of probability, Find sample space of an experiment, Identify the probability of an event

What is the essential question for this lesson on probability?

How can understanding the concept of probability help to make good decisions in different situations, and what real-world situations show the importance of probability?

What is the definition of probability?

Probability is a branch of mathematics that analyzes the chance of a particular event occurring. It aims to predict the likelihood of something happening or not happening.

What is an experiment in the context of probability?

<p>An experiment is any activity that can be repeated under similar conditions.</p> Signup and view all the answers

What is a sample space (S) in probability?

<p>The sample space is the set of all possible outcomes in an experiment.</p> Signup and view all the answers

What is an event (E) in probability?

<p>An event is a subset of a sample space.</p> Signup and view all the answers

What is the formula to calculate the probability of an event?

<p>Probability of an event (p(E)) = Number of outcomes favoring the event / Total number of outcomes, or p(E) = n(E) / n(S)</p> Signup and view all the answers

Match the following experiments with their respective sample spaces:

<p>Tossing a coin = Head or tail Rolling a die = 1, 2, 3, 4, 5, 6 True or False = True or False Tossing two coins = HH, TT, HT, TH</p> Signup and view all the answers

What is the probability of getting a tail when tossing a coin?

<p>1/2 or 50%</p> Signup and view all the answers

What is the probability of getting an even number when rolling a die?

<p>3/6 or 1/2 or 50%</p> Signup and view all the answers

What is the probability of getting two tails when tossing two coins?

<p>1/4 or 25%</p> Signup and view all the answers

What is the total number of the sample space when drawing a card from a standard deck of cards?

<p>52</p> Signup and view all the answers

Study Notes

Introduction to Probability

  • Probability is a branch of mathematics that analyzes the chance of a particular event occurring.
  • Its purpose is to predict the likelihood of something happening or not.

Learning Targets

  • Recall the concept of probability.
  • Identify probability terminology.
  • Determine the sample space of an experiment.
  • Identify the probability of an event.

Essential Questions

  • How does understanding probability help in making sound decisions in various situations?
  • What real-world situations highlight the importance of probability?

Recap of Statistics

  • Statistics is divided into descriptive and inferential statistics.
    • Descriptive statistics focuses on data.
    • Inferential statistics focuses on data variables.
      • Data Variables (discrete or continuous)
        • Quantitative variables
        • Qualitative variables
    • Population (parameter)
    • Sample (statistic)

Name it! (Examples)

  • Dice
  • Playing Cards
  • Coins
  • Money

Probability of an Event

  • Probability is calculated as the ratio of favorable outcomes to the total possible outcomes.

    • Probability = (Number of outcomes favoring the event) / (Total number of outcomes)
    • P(E) = n(E) / n(S)

  • Example: Tossing a coin

    • Probability of getting tails is 1/2 or 50%

  • Example: Rolling a die

    • Probability of getting an even number is 3/6 or 50%

  • Example: Tossing two coins

    • Probability of getting two tails is 1/4 or 25%

  • Example: Drawing a card from a deck of 52 cards.

    • Total possible outcomes = 52
    • Example calculations for card draws are listed in later pages.

Experiment and Sample Space

  • Experiment: An activity that can be repeated under similar conditions.
  • Sample Space (S): The set of all possible outcomes of an experiment.
    • Examples
      • Tossing a coin: Heads or Tails
      • Rolling a die: 1, 2, 3, 4, 5, 6
      • Tossing two coins: HH, HT, TH, TT

Let's Try: Experiments and Questions

  • Tossing three coins
    • How many possible outcomes?
    • What is the sample space?
    • Probability of getting exactly two heads?
    • Probability of getting at least two heads?
    • Probability of getting three heads?
  • Rolling two dice
    • How many possible outcomes?
    • What is the sample space?
    • Probability of getting an even sum?
    • Probability of getting a sum greater than 12?
    • Probability of getting a sum between 1 and 13?

Additional Concepts

  • Define sample space.
  • Formula for finding the probability of an event.
  • Definitions of sample space and events.
  • Difference between sample space and events.

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Related Documents

Introduction to Probability PDF

Description

This quiz covers the fundamental concepts of probability, including terminology, sample space, and event likelihood. Understanding probability is essential for making informed decisions in real-world scenarios. Test your knowledge of both basic and applied probability concepts.

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