P6 Mathematics - Term II

Topic 6: Data Handling

Lesson 6: Probability of Simple Events

Duration: 45 minutes

Learning Objectives

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

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

Probability Words

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 is Probability?

Probability is the measure of how likely an event is to happen

Probability is:

• A number between 0 and 1
• 0 = impossible (never happens)
• 1 = certain (always happens)
• Between 0 and 1 = possible (might happen)

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

The Probability Formula

To calculate probability:

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

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

Example 1: Coin Flip

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: Calculate Probability

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: 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!

The Probability Scale

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 an 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

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!

Real Experimental Example

Bag with 6 red and 4 blue items:

Theoretical:

• P(red) = 6/10 = 3/5 = 0.6
• P(blue) = 4/10 = 2/5 = 0.4

Experiment - Draw 20 times:

• Got red 13 times: P(red) = 13/20 = 0.65
• Got blue 7 times: P(blue) = 7/20 = 0.35

Close to theory! ✓

Where is Probability Used?

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

Probability and Sets

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

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: 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

Remember these:

• Probability is always between 0 and 1 ✓
• All probabilities in a situation add to 1 ✓
• P(something happens) + P(it doesn't happen) = 1 ✓
• If P(event) = 0, it's impossible ✓
• If P(event) = 1, it's certain ✓
• Probability doesn't guarantee exact outcomes ✓

Common Mistakes

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!)

Data Handling Journey 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: Probability

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 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

Assignment:

1. Probability calculations:
   A bag has 20 sweets: 8 orange, 7 lemon, 5 strawberry

   Calculate P(orange), P(lemon), P(strawberry)
   Which flavor are you most likely to pick?

2. Coin experiment:
   Flip a coin 20 times, record with tally marks
   Calculate experimental P(heads) and P(tails)
   Compare to theoretical probability (1/2)

3. Real-life probability:
   Describe three events in your daily life:

   • One that is certain
   • One that is likely
   • One that is unlikely

4. Reflection: What did you learn about data handling?

Expected time: 25-30 minutes

Thank You!

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!