Mathematics - Senior Secondary 2 - Probability (II)

Probability (II)

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TERM: 2ND TERM

WEEK: 10

Class: Senior Secondary School 2
Age: 16 years
Duration: 40 minutes of 5 periods
Subject: Mathematics
Topic: Probability (II)

  • Focus: Independent Events, Complementary Events, Outcome Tables, Tree Diagrams, and Practical Applications of Probabilities in Health, Business, and Population.

SPECIFIC OBJECTIVES:

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

  1. Define independent events and complementary events in probability.
  2. Derive and apply the rules of probability for independent and complementary events.
  3. Draw outcome tables for probability experiments.
  4. Construct tree diagrams for solving probability problems.
  5. Apply probability concepts to real-world scenarios, especially in health, business, and population studies.

 

INSTRUCTIONAL TECHNIQUES:

  • Question and answer
  • Teacher-led discussion
  • Student practice and problem-solving
  • Group work and case studies
  • Demonstrations using outcome tables and tree diagrams

 

INSTRUCTIONAL MATERIALS:

  • Whiteboard and markers
  • Newspaper cut-outs of stock market reports
  • Annual reports of shares
  • Published statistics on capital markets
  • Outcome table worksheets
  • Tree diagram templates

 

PERIOD 1 & 2: Independent and Complementary Events

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction

Introduces the concepts of independent and complementary events. Defines them with examples.

Students listen attentively, take notes, and ask questions.

Step 2 - Independent Events

Explains independent events using examples (e.g., flipping a coin, rolling a die). Derives the probability rule for independent events: P(A ∩ B) = P(A) × P(B).

Students observe and take notes. They brainstorm other examples of independent events.

Step 3 - Complementary Events

Explains complementary events with examples (e.g., flipping a coin: heads or tails). Derives the rule for complementary events: P(A') = 1 - P(A).

Students discuss complementary events in pairs and write down the derived rule.

Step 4 - Question and Answer

Asks questions to assess understanding (e.g., "What happens if two events are independent?")

Students answer the questions and clarify any confusion.

NOTE ON BOARD:

  • Independent Events: Events where the occurrence of one does not affect the other. Example: Flipping a coin and rolling a die.
  • Complementary Events: Events where one event happens if the other does not. Example: If it's not raining, the sun is shining.

 

EVALUATION (5 exercises):

  1. What is the probability of two independent events happening?
  2. If P(A) = 0.3, what is P(A')?
  3. Are the events of drawing a red card and drawing a black card from a deck independent?
  4. Define complementary events with an example.
  5. If two events are complementary, what is the sum of their probabilities?

CLASSWORK (5 questions):

  1. If P(A) = 0.4, what is P(A')?
  2. Are the events “tossing a coin” and “rolling a die” independent?
  3. What is the probability of drawing a face card (King, Queen, Jack) from a deck of cards?
  4. If P(A) = 0.6, find P(A ∩ B) if P(B) = 0.5 and A and B are independent.
  5. If two complementary events are mutually exclusive, what is the sum of their probabilities?

ASSIGNMENT (5 tasks):

  1. List two examples of independent events.
  2. Describe complementary events with a real-life example.
  3. If P(A) = 0.5, what is P(A ∩ B) if A and B are independent and P(B) = 0.3?
  4. Create a scenario where two events are complementary.
  5. Calculate the probability of selecting a white ball from a set of 10 balls where 4 are white and 6 are black.

 

PERIOD 3 & 4: Outcome Tables and Tree Diagrams

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Outcome Tables

Explains outcome tables and demonstrates how to organize all possible outcomes for a given probability experiment.

Students observe the demonstration and take notes.

Step 2 - Outcome Table Construction

Creates a simple outcome table (e.g., flipping two coins) to list all possible outcomes.

Students construct their own outcome tables for given scenarios (e.g., rolling two dice).

Step 3 - Tree Diagrams

Introduces tree diagrams and shows how to use them for solving probability problems.

Students follow along with the tree diagram and understand its structure.

Step 4 - Guided Practice

Provides practice problems using outcome tables and tree diagrams to calculate probabilities.

Students work through the examples and share their answers.

NOTE ON BOARD:

  • Outcome Tables: A table that lists all possible outcomes of a random experiment.
  • Tree Diagrams: A diagram used to represent the possible outcomes of a probability experiment.

 

EVALUATION (5 exercises):

  1. Draw an outcome table for rolling two dice.
  2. Use a tree diagram to show the possible outcomes of flipping two coins.
  3. Calculate the probability of getting two heads when flipping two coins using a tree diagram.
  4. What is the probability of drawing a red card from a deck, followed by a black card?
  5. Create an outcome table for drawing two cards from a deck without replacement.

CLASSWORK (5 questions):

  1. Construct an outcome table for tossing two coins.
  2. Use a tree diagram to find the probability of drawing two red cards from a deck of cards.
  3. What is the probability of selecting a blue ball, then a green ball without replacement, if there are 5 blue balls and 7 green balls?
  4. Construct a tree diagram for drawing two cards from a deck with replacement.
  5. Calculate the probability of rolling a sum of 7 with two dice using an outcome table.

ASSIGNMENT (5 tasks):

  1. Create an outcome table for rolling two dice.
  2. Use a tree diagram to calculate the probability of selecting two red balls from a bag of 3 red and 2 blue balls without replacement.
  3. Calculate the probability of flipping at least one head in three coin tosses.
  4. Use an outcome table to determine the probability of drawing a King, followed by a Queen from a deck.
  5. Construct a tree diagram for a scenario involving a 3-step process with 4 possible outcomes at each step.

 

PERIOD 5: Practical Applications of Probability (Health, Business, Population)

PRESENTATION:

Step

Teacher’s Activity

Student’s Activity

Step 1 - Introduction to Practical Applications

Introduces real-world applications of probability in health, business, and population. Gives examples like predicting disease spread or market analysis.

Students listen attentively and take notes.

Step 2 - Case Study on Health

Presents a case study on the probability of a disease outbreak and its spread based on certain conditions.

Students analyze the case study and discuss their findings.

Step 3 - Case Study on Business

Explains how businesses use probability for decision-making, using stock market reports as an example.

Students examine stock market reports and calculate probabilities for given scenarios.

Step 4 - Case Study on Population

Demonstrates how probability helps estimate population growth or distribution in certain areas.

Students work on a population estimation problem.

EVALUATION (5 exercises):

  1. How can probability be applied to predict the spread of a disease?
  2. How does probability help businesses in decision-making?
  3. What are the key factors to consider when using probability to estimate population growth?
  4. Provide an example of probability used in health statistics.
  5. How would you use probability to predict the success of a business investment?

CLASSWORK (5 questions):

  1. How would you use probability to predict the chance of rainfall tomorrow?
  2. What is the probability that a company’s stock price will rise next year?
  3. How can probability be used to calculate the chances of survival for a disease patient?
  4. Create a simple probability scenario for estimating the number of people with a specific disease.
  5. Use probability to predict the number of defective products in a factory.

ASSIGNMENT (5 tasks):

  1. Research how probability is used in the health sector for disease control.
  2. How does probability help with investment decisions in business?
  3. Use probability to estimate the population of a city in 5 years, given its current growth rate.
  4. Calculate the probability of a patient recovering from a certain disease based on given statistics.
  5. Write a report on how probability can help in risk management in business.