P6 Mathematics - Term II

Topic 6: Data Handling

Lesson 6: Probability of Simple Events

Duration: 45 minutes

Today's Learning Objectives for Probability

By the end of this lesson, you will be able to:

• Define probability and understand it as likelihood
• Identify possible outcomes of simple events
• Calculate simple probabilities using the formula
• Express probability as a fraction or description
• Apply probability concepts to real-life situations

Understanding Chance in Everyday Life

Think about these questions:

• Will the sun rise tomorrow?
• Will it rain today?
• Will you grow wings and fly?

Different levels of certainty!

Certain - Definitely will happen
Possible - Might happen
Impossible - Cannot happen

Words We Use for Probability

Different ways to describe likelihood:

• Certain = Will definitely happen (100% sure)
• Likely/Probable = Good chance of happening
• Unlikely = Small chance of happening
• Impossible = Cannot happen (0% chance)
• Even chance = Equally likely to happen or not

What Does Probability Actually Measure?

Probability is a number between 0 and 1 measuring how likely an event is

• 0 = impossible (never happens)
• 1 = certain (always happens)
• Between = possible (might happen)

Example: Flipping a coin has probability 1/2 for heads

Learning the Probability Formula Now

To calculate probability:

Probability = Number of favorable outcomes
              ──────────────────────────────
              Total number of possible outcomes

In shorter form:
P(event) = Favorable outcomes ÷ Possible outcomes

Example 1: Flipping a Coin

Flipping a coin - what's P(Heads)?

Possible outcomes: Heads or Tails (2 outcomes)
Favorable outcomes: Heads (1 outcome)

Calculate:
P(Heads) = 1/2 = 0.5 = 50%

Same for tails: P(Tails) = 1/2

Example 2: Rolling a Die

Rolling a die - what's P(rolling a 4)?

Possible outcomes: 1, 2, 3, 4, 5, 6 (6 outcomes)
Favorable outcomes: 4 (1 outcome)

Calculate:
P(rolling 4) = 1/6

What about P(even number)?
Even numbers: 2, 4, 6 (3 favorable)
P(even) = 3/6 = 1/2

Example 3: Picking from a Bag

A bag contains:

• 5 red balls
• 3 blue balls
• Total = 8 balls

What's P(picking red)?

Favorable outcomes = 5 red balls
Possible outcomes = 8 total balls
P(red) = 5/8

Practice Calculating Spinner Probability Now

A spinner has 8 equal sections:

• 3 red sections
• 3 blue sections
• 2 yellow sections

Calculate:
a) P(spinning red)
b) P(spinning blue)
c) P(spinning yellow)

Work in your exercise book!

Answers for the Spinner Probabilities

Total sections = 8

a) P(red) = 3/8 (3 red sections out of 8 total)

b) P(blue) = 3/8 (3 blue sections out of 8 total)

c) P(yellow) = 2/8 = 1/4 (2 yellow sections out of 8 total)

Notice: Red and blue have equal probability!

Understanding the Probability Scale Fully

Probability ranges from 0 to 1:

0          1/4         1/2         3/4          1
|-----------|-----------|-----------|-----------|
Impossible  Unlikely    Even      Likely    Certain
                       Chance

Examples:

• Rolling 7 on normal die → 0 (impossible)
• Coin landing heads → 1/2 (even chance)
• Sun rising tomorrow → 1 (certain)

Conducting a Coin Flip Experiment

Let's test probability with coin flips!

Theory: P(Heads) = 1/2

Experiment:

• Flip a coin 10 times
• Record results with tally marks
• Count heads and tails
• Calculate: Heads ÷ Total flips

Does the experiment match the theory?

Experimental vs Theoretical Probability Explained

Two types of probability:

Theoretical: What should happen based on mathematics

• P(Heads) = 1/2 (one out of two outcomes)

Experimental: What actually happens in trials

• Flipped 10 times, got 6 heads
• P(Heads) = 6/10 = 0.6

With many trials, experimental approaches theoretical!

A Real Theoretical vs Experimental Example

Bag with 6 red, 4 blue items:

Theoretical: P(red) = 6/10 = 0.6, P(blue) = 4/10 = 0.4

Experiment (20 draws): P(red) = 13/20 = 0.65, P(blue) = 7/20 = 0.35

Close to theory! ✓

Where Is Probability Used in Life?

Real-life applications:

• Weather: "60% chance of rain tomorrow"
• Sports: Predicting match outcomes
• Medicine: Success rates of treatments
• Insurance: Calculating risk
• Agriculture: Likelihood of good harvest
• Games: Understanding odds and chances

Connecting Probability to Sets Again

Remember sets from Term 1?

All possible outcomes = Universal set

Example: Rolling a die

• Universal set U = {1, 2, 3, 4, 5, 6}
• Even numbers = {2, 4, 6}
• P(even) = 3/6 = 1/2

Probability uses set concepts!

Practice Problem: Picking a Learner

In a class of 30 learners:

• 18 are girls
• 12 are boys

The teacher picks one learner at random.

Calculate:
a) P(picking a girl)
b) P(picking a boy)
c) Express both as decimals

Answers for the Class Probability

Total learners = 30

a) P(girl) = 18/30 = 3/5

b) P(boy) = 12/30 = 2/5

c) As decimals:

• P(girl) = 0.6 or 60%
• P(boy) = 0.4 or 40%

Check: 0.6 + 0.4 = 1.0 ✓

Important Probability Facts to Remember

• Probability is always between 0 and 1
• All probabilities in a situation add to 1
• P(event) + P(not event) = 1
• P = 0 is impossible; P = 1 is certain
• Probability doesn't guarantee exact outcomes

Common Probability Mistakes to Avoid

Avoid these errors:

• Thinking probability predicts exact outcomes
• Confusing "unlikely" with "impossible"
• Forgetting to count all possible outcomes
• Not simplifying fractions ✓
• Thinking past outcomes affect future ones
  (each coin flip is independent!)

Our Data Handling Journey Is Complete!

Six lessons, amazing progress:

1. Data collection and frequency tables
2. Pie charts
3. Line graphs
4. Mean, median, mode
5. Range and data analysis
6. Probability

You now have professional data handling skills!

Summary of Today's Probability Lesson

Key points from today:

• Probability measures how likely events are
• Probability = Favorable ÷ Possible outcomes
• Probability ranges from 0 (impossible) to 1 (certain)
• Theoretical vs experimental probability
• Probability is used everywhere in real life
• Understanding probability helps us make decisions

Celebrating Your Data Handling Achievement

What you can now do:

• Collect and organize data professionally
• Create tables, pie charts, and line graphs
• Calculate and interpret statistics
• Analyze data completely
• Understand and calculate probability

These skills will help you in:
School, work, business, daily decisions, and life!

Homework: Sweets and Coin Experiment

1. Bag of 20 sweets: 8 orange, 7 lemon, 5 strawberry
   Calculate P(orange), P(lemon), P(strawberry)

2. Coin experiment: Flip 20 times, record with tally marks
   Compare experimental P(heads) to theoretical 1/2

Homework: Real-Life Events and Reflection

3. Describe three daily events: one certain, one likely, one unlikely
4. Reflection: What did you learn about data handling?

Expected time: 25-30 minutes

Thank You for Your Hard Work!

You've completed Data Handling!

Next topic: Money

Keep practicing:

• Use data in your daily life
• Notice graphs in newspapers
• Calculate statistics
• Think about probability

Well done on your hard work and progress!