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

Flashcards

Probability

The branch of mathematics that analyzes the chances of events occurring.

Experiment

Any activity that can be repeated under similar conditions.

Sample Space (S)

The set of all possible outcomes in an experiment.

Event (E)

Any subset of a sample space.

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Probability of an Event

The number of outcomes favoring the event divided by the total number of outcomes.

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Data

The specific values that a variable can take on.

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Descriptive Statistics

A way to describe and summarize data.

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Inferential Statistics

Using data from a sample to make inferences about a larger population.

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Parameter

A characteristic of a population.

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Statistic

A characteristic of a sample.

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Discrete Variables

Variables that can be counted.

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Continuous Variables

Variables that can be measured.

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Qualitative Variables

Variables that describe qualities or categories.

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Tossing a coin

The probability of getting heads or tails when tossing a coin.

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Rolling a die

The probability of getting any number from 1 to 6 when rolling a die.

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True or False

The probability of getting either True or False as an outcome.

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Tossing two coins

The probability of getting two heads, two tails, one head and one tail (in either order) when tossing two coins.

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Probability of getting a tail

The probability of getting a tail when tossing a coin.

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Probability of getting and even number

The probability of getting an even number when rolling a die.

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Probability of getting two tails

The probability of getting two tails when tossing two coins.

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Drawing a card from a deck

Think of an ordinary deck of cards with 52 cards.

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Probability of drawing a red card

Probability of drawing a red card from a deck.

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Probability of drawing a diamond card

Probability of drawing a diamond card from a deck.

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Probability of drawing an ace of clubs

Probability of drawing an ace of clubs from a deck.

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Probability of drawing a king card

Probability of drawing a king card from a deck.

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Probability of drawing a card that is not a face card

Probability of drawing a card that is not a face card.

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Tossing three coins

The number of possible outcomes when tossing three coins.

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Probability of getting exactly two heads

The probability of getting exactly two heads when tossing three coins.

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Probability of getting at least two heads

The probability of getting at least two heads when tossing three coins.

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Probability of getting three heads

The probability of getting three heads when tossing three coins.

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Rolling two dice

The number of possible outcomes when rolling two dice.

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Probability of getting an even sum

The probability of getting an even sum when rolling two dice.

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Probability of getting a sum higher than 12

The probability of getting a sum higher than 12 when rolling two dice.

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Probability of getting a sum between 1 and 13

The probability of getting a sum between 1 and 13 when rolling two dice.

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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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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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