Higher June 2018 Unit 2 Q16
16. A bag contains 200 beads.
Some of the beads are red.
A bead is selected at random.
Its colour is recorded and then the bead is replaced.
A second bead is selected at random and its colour is also recorded.
The probability that two red beads are selected is 0·1369.
Calculate the number of red beads in the bag. [4]
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{n}{200} \times \dfrac{n}{200} = 0.1369\) | M2 | Award M1 for P(Red)×P(Red)=0.1369 or equivalent, e.g. R(ed)×R(ed)=0.1369; P2=0.1369, etc. Where \(n\) is the number of red beads. |
| \((n^2 =)\ 200 \times 200 \times 0.1369\) OR \((n =)\sqrt{200 \times 200 \times 0.1369}\) | m1 | |
| (Number of red beads=) 74 | A1 |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| P(Red)×P(Red)=0.1369 or equivalent, | M1 | e.g. R(ed)×R(ed)=0.1369; P2=0.1369, etc. |
| (P(Red) =) \(\sqrt{0.1369}(= 0.37)\) | m1 | |
| (Number of red beads=) \(\sqrt{0.1369}\)×200 | m1 | |
| = 74 | A1 | If an answer 74/200 is offered award M3A0, but ’74 out of 200’ gains full marks. |