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 and nothing else.
Kim takes at random two counters from the bag. She does not replace the first counter before taking the second.
Work out the probability that the two counters are different colours.
Give your answer as a fraction in its simplest form. (4 marks)Level 4 · 4 marksTry it - 2A bag contains 5 white counters and 4 black counters.
Three counters are taken from the bag at random, without replacement.
(a) Work out the probability that all three counters are white.
(b) Work out the probability that all three counters are the same colour.Level 4 · 6 marksTry it - 3A bag contains 5 green counters and 7 yellow counters.
Two counters are taken from the bag at random, without replacement.
Jack writes:
(a) Explain what is wrong with the second fraction in Jack's working.
(b) Work out the correct probability that both counters are green.Level 4 · 3 marksTry it - 4A tin contains 10 biscuits.
3 of the biscuits are chocolate and the other 7 are plain.
Three biscuits are taken from the tin at random, without replacement.
Work out the probability that at least one of the three biscuits is chocolate.Level 4 · 4 marksTry it - 5A bag contains only green counters and white counters.
The probability that a counter taken at random from the bag is green is .
There are 15 white counters in the bag.
(a) Show that there are 24 counters in the bag.
(b) Two counters are taken from the bag at random, without replacement.
Work out the probability that the two counters are the same colour.Level 4 · 6 marksTry it