GCSE · Combined events & tree diagrams

Probability without replacementExam-style questions

Why the second pick happens in a smaller, changed bag — so the total always drops by one but a colour's count drops only if that colour was taken — and how that turns "one of each", "at least one" and the reverse quadratic questions.

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17 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
There are $10$ cards numbered $1$ to $10$ . A card is taken and not replaced; it is the $7$ . Write down the probability that the next card taken is an even number.
Level 1 · 1 markTry it
2
A box has $4$ red and $6$ green pens. One pen is taken and not put back. It is red. Write down the probability that the next pen taken is also red.
Level 1 · 1 markTry it