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+---- Thread: Probability Fundamentals — Understanding Chance Clearly (/showthread.php?tid=62)
Probability Fundamentals — Understanding Chance Clearly - Leejohnston - 11-13-2025
Probability Fundamentals — Understanding Chance Clearly
Probability is the mathematics of chance.
It tells us how likely something is to happen.
GCSE probability is easier than it looks once you understand the basics — and this guide explains everything clearly.
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1. What Is Probability?
Probability is always a number between 0 and 1:
• 0 = impossible
• 1 = certain
• 0.5 = 50% chance
We can write probability as:
• fractions → 1/4
• decimals → 0.25
• percentages → 25%
All three mean the same thing.
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2. Probability Formula
Probability = (number of desired outcomes) ÷ (total number of outcomes)
Example:
A bag contains 5 red sweets and 3 blue sweets.
Probability of picking red = 5/8.
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3. Complementary Probabilities
Two outcomes that cover ALL possibilities are complements.
P(A) + P(not A) = 1
Example:
If P(rain) = 0.3
Then P(no rain) = 1 – 0.3 = 0.7
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4. Mutually Exclusive Events
Events that cannot happen at the same time.
Example: rolling a die:
You cannot roll a 3 AND a 5 at the same time.
So:
P(A or B) = P(A) + P(B)
Example:
P(rolling a 2 or a 4) = 1/6 + 1/6 = 2/6 = 1/3
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5. Independent Events
Two events that do not affect each other.
Example:
Flipping a coin twice.
P(A and B) = P(A) × P(B)
Example:
P(Heads then Heads) = 1/2 × 1/2 = 1/4
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6. Dependent Events
Events where the first changes the second.
Example:
Picking two sweets *without replacement*.
Bag: 5 red, 3 blue → total 8
P(red then blue)
= (5/8) × (3/7)
= 15/56
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7. Probability Scale
Helps visualise chance:
0 ─── 0.25 ─── 0.5 ─── 0.75 ─── 1
Impossible … Unlikely … Even … Likely … Certain
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8. Common GCSE Mistakes
❌ Adding probabilities when you should multiply
❌ Forgetting the total changes after removing an item
❌ Mixing fractions with percentages
❌ Assuming events are independent when they’re not
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Summary
Key rules to remember:
• Probability = desired ÷ total
• Complements add to 1
• Mutually exclusive → add
• Independent → multiply
• Dependent → total changes
Master these and every GCSE probability question becomes manageable.