Foundation November 2020 Unit 1 Q18
18. 80 cards are placed in a box.
Each card shows a picture of one of four islands near the coast of Wales:
Bardsey Island, Ramsey Island, Skomer Island or Puffin Island.
A card is chosen at random from the box.
The table below gives some of the probabilities that the chosen card shows a picture of a particular island.
| Island | Bardsey Island (Ynys Enlli) | Ramsey Island (Ynys Dewi) | Skomer Island (Ynys Sgomer) | Puffin Island (Ynys Seiriol) |
|---|---|---|---|---|
| Probability | 0·4 | 0·15 | 0·25 |
How many of the 80 cards show a picture of Puffin Island?
You must show all your working. [4]
| Scheme | Marks | Comments |
|---|---|---|
| (Probability of Puffin Island=)1 − 0·4 − 0·15 − 0·25 | M1 | An unsupported answer of 0·56 implies M1 |
| = 0·2 | A1 | |
| (Number of cards showing Puffin Island =) 0·2 × 80 | M1 | FT ‘their stated P(Puffin Island)’ × 80, only if ‘their stated P(Puffin Island)’ < 1. |
| = 16 | A1 | 16/80 is M1A0 unless 16 has been seen. |
Alternative method
| Scheme | Marks | Comments |
|---|---|---|
| (Number of cards showing other 3 islands =) 0·4 × 80 + 0·15 × 80 + 0·25 × 80 or equivalent | M1 | Allow M1 for sight of 32 AND 12 AND 20. |
| = 64 | A1 | |
| (Number of cards showing Puffin Island =) 80 – 64 | M1 | FT 80 − ‘their derived 64’, only if ‘their derived 64’<80. |
| = 16 | A1 | 16/80 is M1A0 unless 16 has been seen. |