Probability (I) - Throwing of Dice, Tossing of Coin, Pack of Playing Cards, Theoretical and Experimental

Grade 11 · Mathematics

Semester 2 | Period 5 | Week 27

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Subject: Mathematics

Semester: 2

Period: 5

Week: 27

WEEK 27
Class: Grade 11
Age: 16 years
Duration: 40 minutes per period (5 periods)
Subject: Mathematics
Topic: Probability (I) - Throwing of Dice, Tossing of Coin, Pack of Playing Cards, Theoretical and Experimental Probability, Mutually Exclusive Events

SPECIFIC OBJECTIVES:

By the end of the lesson, students should be able to:

  1. Understand the concept of probability.
  2. Identify and describe the instruments of chance (coin, die, pack of playing cards).
  3. Calculate theoretical probability using the coin, die, and pack of cards.
  4. Calculate experimental probability through practical exercises (tossing coins, throwing dice).
  5. Recognize and explain mutually exclusive events.

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Guided demonstration
  • Discussion
  • Hands-on activity
  • Practice exercises
  • Use of analogy

INSTRUCTIONAL MATERIALS:

  • Ludo
  • Dice
  • Pack of playing cards
  • Whiteboard and markers
  • Worksheets for practice

PERIOD 1 & 2: Introduction to Probability (Throwing of Dice, Tossing of Coin, Pack of Playing Cards)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1

Introduces the concept of probability and defines it as the likelihood of an event occurring. Uses practical examples (coin toss, die throw).

Students listen and ask questions.

Step 2

Displays a coin, die, and pack of cards. Discusses the number of faces on the coin (2), die (6), and cards (52). Leads students to identify instruments of chance.

Students observe the objects, participate in identifying the number of faces or cards.

Step 3

Explains the difference between theoretical and experimental probability. Provides examples for each, using the die and coin.

Students listen, take notes, and ask clarifying questions.

Step 4

Demonstrates throwing the die and tossing the coin. Records the results, then explains how to calculate experimental probability.

Students observe and record results.

NOTE ON BOARD:

  • Theoretical Probability: Probability of an event occurring = (Number of favorable outcomes) / (Total possible outcomes)
  • Experimental Probability: Probability based on the actual outcome of experiments.
  • Mutually Exclusive Events: Events that cannot occur at the same time (e.g., flipping a coin and getting both heads and tails).

EVALUATION (5 exercises):

  1. What is the probability of tossing heads on a coin?
  2. What is the probability of rolling a 4 on a die?
  3. Define theoretical probability.
  4. What is the total number of cards in a standard deck?
  5. Give an example of two mutually exclusive events.

CLASSWORK (5 questions):

  1. Calculate the probability of rolling an even number on a die.
  2. What is the probability of tossing tails on a coin?
  3. If a die is rolled, what is the probability of rolling a number greater than 4?
  4. How many red cards are there in a deck of playing cards?
  5. If two dice are thrown, what is the probability of rolling a sum of 7?

ASSIGNMENT (5 tasks):

  1. Calculate the probability of drawing a face card from a deck of playing cards.
  2. Toss a coin 20 times and calculate the experimental probability of getting heads.
  3. Roll a die 30 times and calculate the experimental probability of rolling a 3.
  4. Explain what is meant by mutually exclusive events.
  5. Calculate the theoretical probability of getting a number divisible by 3 when rolling a die.

PERIOD 3 & 4: Theoretical and Experimental Probability

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1

Reviews the concepts of theoretical and experimental probability.

Students review their notes and ask for clarification on any confusing points.

Step 2

Guides students through a practical activity: Toss a coin 30 times, record outcomes, and calculate experimental probability.

Students perform the experiment, recording the results and calculating the experimental probability.

Step 3

Similarly, has students roll a die 50 times, recording outcomes to calculate experimental probability.

Students perform the experiment, recording the results and calculating the experimental probability.

Step 4

Discusses any discrepancies between theoretical and experimental probabilities.

Students discuss their findings and reflect on the differences between the theoretical and experimental results.

NOTE ON BOARD:

  • Theoretical Probability Example (Coin): P(Heads) = 1/2, since there are 2 possible outcomes and only 1 favorable outcome.
  • Experimental Probability Example (Coin Toss): P(Heads) = (Number of Heads) / (Total Tosses).

EVALUATION (5 exercises):

  1. After tossing a coin 50 times, how many heads would you expect to see?
  2. After rolling a die 20 times, what is the probability of rolling a 5?
  3. Calculate the experimental probability of getting a red card from a deck of playing cards if 10 cards are drawn.
  4. If 2 dice are thrown, what is the probability of not rolling a 6?
  5. After 100 coin tosses, what should be the expected number of tails?

CLASSWORK (5 questions):

  1. Toss a coin 15 times and calculate the probability of getting tails.
  2. Roll a die 25 times and calculate the probability of getting a number greater than 4.
  3. Calculate the experimental probability of drawing a black card from a deck after 20 draws.
  4. If a coin is tossed 50 times, what is the theoretical probability of getting heads?
  5. After 30 rolls of a die, what is the probability of rolling an odd number?

ASSIGNMENT (5 tasks):

  1. Perform an experiment by tossing a coin 50 times and record your results. Calculate the experimental probability of getting heads.
  2. Calculate the probability of drawing a queen from a deck of cards.
  3. Perform an experiment by rolling a die 60 times and calculate the experimental probability of rolling a number less than 4.
  4. Explain the difference between theoretical and experimental probability.
  5. If a deck of cards is shuffled and a card is drawn at random, what is the theoretical probability of drawing a spade?

PERIOD 5: Mutually Exclusive Events

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1

Defines mutually exclusive events. Gives examples, such as the outcome of a coin toss (heads or tails).

Students listen, observe, and ask questions for clarification.

Step 2

Explains how to calculate probabilities for mutually exclusive events. Demonstrates with examples, such as the probability of rolling a 2 or 4 on a die.

Students take notes and work through examples provided by the teacher.

Step 3

Discusses how to use the Addition Rule for Mutually Exclusive Events: P(A or B) = P(A) + P(B).

Students solve sample problems with the teacher.

Step 4

Provides practice exercises for students to work on in pairs.

Students practice solving problems on mutually exclusive events.

NOTE ON BOARD:

  • Mutually Exclusive Events: Two events that cannot occur at the same time.
  • Addition Rule for Mutually Exclusive Events: P(A or B) = P(A) + P(B).

EVALUATION (5 exercises):

  1. What is the probability of drawing either a heart or a club from a deck of cards?
  2. If two dice are rolled, what is the probability of rolling a 1 or a 5?
  3. Can you have a mutually exclusive event with a coin toss? Explain.
  4. Calculate the probability of drawing a red card or a face card from a deck of cards.
  5. What is the probability of rolling a number less than 4 or greater than 4 on a die?

CLASSWORK (5 questions):

  1. If a coin is tossed, what is the probability of landing on heads or tails?
  2. Calculate the probability of drawing a black card or a queen from a deck of cards.
  3. If a die is rolled, what is the probability of rolling a 3 or a 5?
  4. Calculate the probability of rolling a number divisible by 2 or 3 on a die.
  5. If two dice are rolled, what is the probability of rolling a sum of 2 or 12?

ASSIGNMENT (5 tasks):

  1. Calculate the probability of drawing a red card or an even-numbered card from a deck of cards.
  2. If a die is rolled, what is the probability of rolling a 1 or a 2?
  3. Explain why it is impossible to have two mutually exclusive events occur at the same time.
  4. Calculate the probability of rolling a 3 or a 6 on a die.
  5. Give an example of two mutually exclusive events in a real-life scenario.