Probability equations

Objective. Form and solve algebraic probability constraints.

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2. Worked example
3. Practice
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Learn: the key idea

Probability equations translate a word problem involving unknown probabilities into algebraic equations, often using the fact that all outcomes sum to 1 or that two expressions must be equal. Assign a letter to the unknown probability or frequency, write an equation from the given condition, then solve it like any other algebraic equation. Checking the solution gives sensible probabilities between 0 and 1 is an essential final step. If a bag has x red, 2x blue and 3 green counters totalling 15, solve x + 2x + 3 = 15 to get x = 4. This blends algebra skills directly with probability reasoning.

Worked example

A spinner has three sections coloured red, blue and green. P(red) = x, P(blue) = 2x and P(green) = 0.1. Find x.

1 $Use the fact probabilities sum to 1$
2 $x + 2x + 0.1 = 1$
3 $3x = 0.9$
4 $x = 0.3$

Answer: 0.3

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Common mistake. A common mistake is forgetting to include every category when forming the total-sums-to-one equation, such as omitting a stated 'green' probability, which produces an equation that cannot be solved correctly.

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