Solving Problems Using Outcomes of Experiments

Content Standards and Learning Competencies

Content Standards

The learners should have knowledge and understanding of outcomes from experiments.

Performance Standards

By the end of the lesson, the learners are able to gather data from experiments and represent the data in different forms.

Learning Competencies

1. Express outcomes in words and/or symbols and represent outcomes in tables and/or graphs.

2. Solves problems using the outcomes of experiments.

Learning Objectives

Identify Possible Outcomes

Accurately identify all the possible outcomes in an experiment using systematic listing.

Solve Outcome Problems

Correctly solve problems involving outcomes in an experiment using systematic listing.

Apply Experimental Results

Accurately solve problems using the outcomes of experiments.

Illustrate Probability

Correctly illustrate the probability of simple events.

Solve Probability Problems

Accurately solve problems involving the probability of simple events.

Key Concepts Recap

Probability Definition

Probability measures how likely an event is to happen. It is expressed as a number between 0 and 1: - 0 means the event is impossible. - 1 means the event is certain. - A fraction or decimal between 0 and 1 represents the likelihood of an event occurring.

Probability Formula

Formula for Probability of a Simple Event: P(E) = Number of Favorable Outcomes / Total Number of Outcomes

Sample Space

Sample Space (S): The set of all possible outcomes in an experiment.

Simple Event

Simple Event: An event that consists of only one outcome from the sample space.

Examples of Probability in Action

Flipping a Coin

- Sample Space: {Heads, Tails}

- Probability of getting heads: 1/2

Rolling a Die

- Sample Space: {1, 2, 3, 4, 5, 6}

- Probability of rolling a 4: 1/6

- Probability of rolling an even number: 3/6 = 1/2

Drawing a Card

- Probability of drawing a King: 4/52 = 1/13

- Probability of drawing a red card: 26/52 = 1/2

Illustrating Probability of Simple Events

Tree Diagrams

Shows all possible outcomes visually.

Tables and Grids

Organizes results for experiments with multiple steps.

Probability Line

Represents event likelihoods from 0 to 1.

Solving Problems Using Probability

List the Sample Space

Identify all possible outcomes.

Count Favorable Outcomes

Identify the number of ways the event can occur.

Use the Probability Formula

Divide the number of favorable outcomes by the total outcomes.

Example Problem

A bag contains 4 red, 3 blue, and 3 green marbles. What is the probability of drawing a blue marble?

Problem Statement

A bag contains 4 red, 3 blue, and 3 green marbles. What is the probability of drawing a blue marble?

Identify Total Outcomes

Total marbles = 4 + 3 + 3 = 10

Count Favorable Outcomes

Favorable outcomes (blue) = 3

Calculate Probability

P(blue) = 3/10

Lesson Purpose

Apply Probability to Solve Problems

Use probability concepts to answer real-world questions.

Illustrate Probability in Different Ways

Represent probability using diagrams, tables, and lines.

Determine the Probability of Simple Events

Calculate likelihood using the probability formula.

Understand the Concept of Probability

Define probability and its importance in real life.

Key Vocabulary

Probability – A measure of how likely an event is to happen, expressed as a fraction, decimal, or percentage.

Simple Event – An event that consists of only one outcome from the sample space.

Experiment – A process or action that produces a set of outcomes (e.g., rolling a die, flipping a coin).

Sample Space (S) – The set of all possible outcomes in an experiment.

Favorable Outcomes – The outcomes that satisfy a given condition or event.

Probability Formula – P(E) = Number of Favorable Outcomes / Total Number of Outcomes

More Key Vocabulary

Certain Event

An event that is guaranteed to happen, with a probability of 1 (100%).

Impossible Event

An event that can never happen, with a probability of 0.

Equally Likely Events

Events that have the same probability of occurring.

Likely Event

An event with a probability greater than 50% but less than 100%.

Unlikely Event

An event with a probability greater than 0% but less than 50%.

Theoretical Probability

Probability determined by mathematical reasoning rather than actual experiments.

Advanced Probability Concepts

Experimental Probability

Probability calculated based on actual trials or experiments.

Tree Diagram

A visual representation of all possible outcomes of an experiment.

Mutually Exclusive Events

Events that cannot happen at the same time (e.g., getting heads and tails in a single coin toss).

Probability and Simple Events

A simple event is an event with only one specific outcome.

Example 1: Flipping a Coin

- Possible outcomes: Heads (H) or Tails (T)

- Each outcome is equally likely.

- The probability of getting heads: P(H) = 1/2

Example 2: Rolling a Die

- Possible outcomes: 1, 2, 3, 4, 5, 6

- Probability of rolling a 3: P(3) = 1/6

Example Probability Calculation

Problem

A bag contains 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a red marble?

Total Marbles

5 + 3 + 2 = 10

Favorable Outcomes

Red marbles = 5

Probability

P(red) = 5/10 = 1/2

Types of Probability Events

1

Certain Event

An event that will always happen. Example: The sun rising tomorrow.

0

Impossible Event

An event that can never happen. Example: Rolling a 7 on a six-sided die.

0.75

Likely Event

More than half the time. Example: Drawing a black card from a deck (26/52 = 50%).

0.25

Unlikely Event

Less than half the time. Example: Rolling a 1 on a die (1/6).

Evaluation Questions

1. What is the probability of rolling a number greater than 4 on a standard six-sided die? (Answer: B - 2/6 or 1/3)

2. A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of randomly picking a red marble? (Answer: D - 5/10 or 1/2)

3. If you flip a fair coin, what is the probability that it lands on tails? (Answer: C - 1/2)

4. A deck of 52 playing cards has 13 spades, 13 hearts, 13 diamonds, and 13 clubs. What is the probability of drawing a heart? (Answer: D - 13/52 or 1/4)

5. A spinner is divided into 4 equal sections: red, blue, green, and yellow. What is the probability that it lands on blue? (Answer: B - 1/4)