📖 The Lesson
Probability tells you how likely something is to happen. On the GED, probability almost always means writing a fraction — the thing you want on top, the total on the bottom. That's the whole idea. Once you can do that, you can handle compound probability and the slightly trickier "without replacement" problems too.
The main point: Probability = favorable outcomes ÷ total outcomes. Write it as a fraction. Simplify it. That gets you through most probability questions on the GED.
Part 1 — The Probability Formula
Probability = favorable outcomes ÷ total outcomes
The top number is what you're looking for.
The bottom number is everything that could happen.
Example — marbles:
A bag has 3 blue marbles and 7 red marbles. What is the probability of picking blue?
Favorable = 3 blue | Total = 10 marbles
Probability of blue = 310
Example — spinner:
A spinner has 8 equal sections: 2 yellow, 3 green, 3 purple. What is the probability of landing on green?
Probability of green = 38
Part 2 — Always Simplify
Divide top and bottom by the same number.
The GED almost always wants the simplified form. If both numbers share a common factor, divide both by it.
Example:
Probability = 48 — divide both by 4 — simplified: 12
Example:
Probability = 69 — divide both by 3 — simplified: 23
Quick check: Use your calculator. Divide top ÷ bottom. If two fractions give the same decimal, they're equivalent.
When a question asks for the probability of two things happening, you multiply. Here's how.
Compound Probability
Probability of A and B = Probability of A × Probability of B
When two events are independent (one doesn't affect the other), multiply their probabilities.
Example — two coin flips:
Probability of heads = 12
Probability of heads AND heads = 12 × 12 = 14
Without Replacement
After the first pick, the total drops by 1.
If an item is removed and not put back, the bottom number on the second pick goes down by 1. If it was what you wanted, the top number drops too.
Example — 5 red, 3 blue (8 total):
First pick: 58 Second pick: 47
Probability of both red = 58 × 47 = 514
Watch out: The most common mistake on without-replacement problems is forgetting to reduce the total after the first pick. The bottom number must drop by 1. If the removed item was what you were looking for, the top number also drops by 1.
🔢 Worked Examples
Example 1 — Basic probability
A drawer has 5 black socks and 5 white socks. What is the probability of randomly picking a white sock?
Favorable = 5 (white socks)
Total = 10 (all socks)
Probability of white = 510
Simplify: divide both by 5 = 12
Example 2 — Compound probability
You flip a coin twice. What is the probability of getting heads both times?
Probability of heads on flip 1 = 12
Probability of heads on flip 2 = 12
Probability of heads AND heads = 12 × 12
= 14
Example 3 — Without replacement
A bag has 6 green and 4 orange marbles. You pick one marble and keep it. What is the probability of picking two green marbles?
First pick: probability of green = 610
One green removed — 5 green left, 9 total
Second pick: probability of green = 59
Probability of both green = 610 × 59 = 3090
Simplify: 3090 = 13
✏️ Practice Questions