Foundation June 2017 Paper 2 Q31
31. Huw and Catrin are playing a game where Huw rolls an ordinary six-sided dice and Catrin spins a fair five-sided spinner, numbered 1, 2, 3, 4 and 5 as shown.
Show that the probability that they both show the same number is \(\dfrac{1}{6}\). [3]
| Scheme | Marks | Comments | ||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Diagram or listing to show all the possible outcomes. e.g.
| M2 | M1 for identifying 11, 22, 33, 44, 55. M1 for identifying that there are 30 possible outcomes. | ||||||||||||||||||||||||||||||||||||||||||
| \(= \frac{5}{30}\) \(\left(= \frac{1}{6}\right)\) | A1 | CAO | ||||||||||||||||||||||||||||||||||||||||||
| (3) |
Alternative
Alternative MS:
| Scheme | Marks |
|---|---|
| Probability of both landing on the same particular number \(= \frac{1}{5} \times \frac{1}{6}\) | M1 |
| Probability of both landing on any same number \(= 5 \times \frac{1}{5} \times \frac{1}{6}\) | M1 |
| \(= \frac{5}{30}\) \(\left(= \frac{1}{6}\right)\) | A1 |
Corrected by Westie's Workshop
- The board's mark scheme printed “34”. Changed to “35” because row 3, column 5 of the grid is dice 3 with spinner 5, which gives the outcome 35.
Original: see the board's mark scheme PDF (link above).