4MA0 Foundation June 2014 Paper 1 Q12
12 In a game, a fair coin is spun and a fair 6-sided dice is rolled.
A score is given according to the rules below.
coin lands on heads
score = 2 × number on the dice coin lands on tails
score = 1 + number on the dice
(a) Complete the table to show all the possible scores.
(2)
| Dice | ||||||
|---|---|---|---|---|---|---|
| Coin | 1 | 2 | 3 | 4 | 5 | 6 |
| Heads | 10 | |||||
| Tails | 4 | |||||
Peter plays the game once.
(b) Find the probability that Peter’s score is 4 (2)
George plays the game 60 times.
(c) Work out an estimate for the number of times George’s score is 10 (2)
| Scheme | Marks |
|---|---|
| Heads 2 4 6 8 (10) 12 Tails 2 3 (4) 5 6 7 | B2 |
| (2) |
Notes
B2: All values correct
If not B2 then B1 for one row correct or a maximum of 2 errors
| Scheme | Marks |
|---|---|
| M1 ft | |
| 2/12 oe | A1 ft |
| (2) |
Notes
M1 ft: ft from their table. Accept \(\dfrac{\text{"2"}}{a}\) with \(a \gt\) "2" or \(\dfrac{b}{12}\) with \(b \lt 12\)
A1 ft: Accept decimal equivalents to 2 dp or better (rounded or truncated)
| Scheme | Marks |
|---|---|
| "1"/12 × 60 or oe | M1 ft |
| 5 | A1 ft |
| (2) | |
| (6 marks) |
Notes
M1 ft: ft from their table