Higher January 2020 Paper 2 Q6
6 A bag contains only red beads, blue beads, green beads and yellow beads.
The table gives the probabilities that, when a bead is taken at random from the bag, the bead will be blue or the bead will be yellow.
| Colour | red | blue | green | yellow |
|---|---|---|---|---|
| Probability | 0.24 | 0.31 |
The probability that the bead will be green is twice the probability that the bead will be red.
Sofia takes at random a bead from the bag.
She writes down the colour of the bead and puts the bead back into the bag.
She does this 180 times.
Work out an estimate for the number of times she takes a red bead from the bag.
(4)
| Scheme | Marks |
|---|---|
| 1 – (0.24 + 0.31) (= 0.45) Or (0.24 + 0.31) × 180 (= 99) | M1 |
| ‘0.45’ ÷ 3 (= 0.15) Or ‘0.45’ × 180 (= 81) Or 180 − 99 (= 81) | M1 |
| ‘0.15’ × 180 Or ‘81’ ÷ 3 | M1 |
| 27 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: or for a correct equation for missing values eg
\(x + 0.24 + 2x + 0.31 = 1\) oe
(can be implied by 2 probabilities that total 0.45 in table if not contradicted in working space)
M1: (or 0.15 correctly placed in table as long as not contradicted)
M1: or for an answer of \(\dfrac{27}{180}\)