Probability and Algebra

This lesson combines probability with algebra — setting up and solving equations from probability statements, working with unknowns in probability problems, and tackling "show that" or proof questions. These are primarily Higher tier topics on the Edexcel GCSE Mathematics (1MA1) specification and often appear as the final parts of 5–6 mark questions.

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Setting Up Equations from Probability Statements

Many Edexcel questions present probability information in words and require you to form and solve an equation.

General Approach

1. Let the unknown be a variable (usually x or n).
2. Write expressions for the number of favourable outcomes and the total number of outcomes.
3. Set up an equation using the given probability.
4. Solve for the unknown.

Worked Example 1

A bag contains x red counters and 8 blue counters. A counter is chosen at random. The probability that it is red is 3/7. Find the value of x.

Solution:

P(red) = x / (x + 8)

Set this equal to 3/7: x / (x + 8) = 3/7

Cross-multiply: 7x = 3(x + 8) 7x = 3x + 24 4x = 24 x = 6