Probability language, frequency trees and expectation
3 exam-style questions. Answers and the mark for each step are on the last page.
- Question 1
(a) A counter is taken from a bag, its colour is recorded, and it is replaced. This is repeated 40 times. Red is recorded 17 times and blue 14 times. Every other result is yellow. How many times is yellow recorded?
- Question 2
36 pupils are invited to a club. 27 attend, including 15 boys. Everyone attending is recorded as either a boy or a girl.
(a) Find the number of girls attending.
(b) A pupil from the invited group is selected at random. Find the probability they attended.
- Question 3
A biased dice is thrown. The probabilities of 1, 2, 3, 4 and 5 are each 0.15. At a fair, each throw costs 60p. A player who throws a 6 wins £2. Otherwise the player wins nothing.
(a) The dice is thrown 300 times. Work out an estimate of the organiser's profit.
Answers and marks
Question 1
(a)
- P1 Establishing or an equivalent valid method.
- A1 Correct answer:
Question 2
(a)
- M1 Subtract boys from the total attending.
- A1 Correct answer:
(b)
- M1 Use the invited group, not only attendees, as the sample space.
- A1 Correct answer:
Question 3
(a) £30
- P1 Finding .
- P1 Expected number of wins, 75.
- P1 Both totals: £180 taken and £150 paid out.
- A1 Correct answer: £30.