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.
17 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try
- 1A bag contains red counters and 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 - 2A box contains 7 red pens and 5 blue pens.
Two pens are taken from the box at random, without replacement.
(a) Work out the probability that both pens are red.
(b) Work out the probability that one pen is red and the other pen is blue.Level 3 · 5 marksTry it - 3A pencil case contains 9 pencils.
4 of the pencils are blue and the other 5 are black.
Kofi takes two pencils at random from the pencil case, without replacement.
Work out the probability that at least one of the two pencils is blue.Level 3 · 3 marksTry it