6 exam-style questions with full mark schemes and model answers. Write your own answer and the AI examiner marks it against the mark scheme.
A bag contains 5 red counters and 3 blue counters. Two counters are taken from the bag at random, one after the other, without replacement.
(a) Work out the probability that both counters are red. (2 marks)
(b) Work out the probability that the two counters are the same colour. (3 marks)
In a year group of 30 students, 18 study French, 14 study German, and 6 study both French and German.
(a) Work out how many students study neither French nor German. (2 marks)
(b) One of the 30 students is chosen at random. Work out the probability that the student studies French but not German. (2 marks)
Two fair six-sided dice are rolled and their scores are added together.
(a) Work out the probability that the total is 9. (2 marks)
(b) Work out the probability that the total is greater than 9. (2 marks)
A spinner has four sections coloured red, green, blue and yellow. The probability of landing on each colour is shown in the table, but the probability for yellow is missing.
| Colour | Red | Green | Blue | Yellow |
|---|---|---|---|---|
| Probability | 0.30 | 0.25 | 0.15 | ? |
(a) Work out the probability of the spinner landing on yellow. (2 marks)
(b) The spinner is spun 200 times. Work out the expected number of times it lands on red. (1 mark)
A four-sided spinner is spun 80 times. It lands on the number 4 a total of 26 times. Work out the relative frequency of landing on 4, giving your answer as a decimal. (2 marks)
The probability that it rains on a particular day is 0.18. Write down the probability that it does not rain on that day. (1 mark)