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
3
A bag contains 4 mint sweets and 6 toffee sweets.

Priya takes a sweet at random and eats it. She then takes a second sweet at random.

(a) Work out the probability that both sweets are mint.

(b) Work out the probability that both sweets are toffee.
Level 2 · 4 marksTry it
4
A bag has $5$ sweets: $2$ orange and $3$ lemon. Two sweets are taken without replacement. Work out the probability that both are lemon.
Level 2 · 2 marksTry it
5
A bag contains $4$ red counters and $6$ blue counters. Two counters are taken at random without replacement.

(a) Work out the probability that both counters are blue. [2]

(b) Work out the probability that the counters are different colours. [2]
Level 3 · 4 marksTry it

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