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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.
Question 1
5 marksThere 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
Why do we multiply probabilities when a question asks for "both counters are blue"?
Revision notes for Edexcel GCSE Maths Probability Equation Questions. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.
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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?
