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Probability Equation Questions

Probability Equation Questions

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Probability trees comparing blue then blue with replacement and without replacement from a bag with 3 red and x blue counters Probability equation questions turn words about counters into algebra. The challenge is usually not the multiplying, but writing the correct fractions before you solve.

Each fraction is "favourable over total". If a question says "both blue", treat it as two events in a row and multiply using the following multiplication rule:

P(A and B)=P(A)×P(B after A) P(A \text{ and } B)=P(A)\times P(B \text{ after } A) P(A and B)=P(A)×P(B after A)

With replacement, the bag resets before the second pick, so the two fractions can be the same. Without replacement, the total drops by 1, and the colour count may also drop by 1.

Questions

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28 exam-style questions

Practice questions

Question 1

5 marks

There are some red counters and some blue counters in a bag.

The ratio of red counters to blue counters is 3:1.

Two counters are removed at random.

The probability that both the counters taken are blue is 120\displaystyle \frac{1}{20}201​

Probability Equation Questions Revision Guide

  1. GCSE
  2. /Maths
  3. /Probability Equation Questions

Revision notes for Edexcel GCSE Maths Probability Equation Questions: explanations and worked examples.

Revision guides

Practise questions

1 of 5

A bag contains xxx blue counters and 5 red counters. Two counters are taken without replacement, and the probability that both are blue is 310\frac{3}{10}103​. Which equation should you write?