Foundation November 2017 Unit 1 Q17
17. Sara is in charge of a game at her school’s Christmas party.
Two fair spinners are spun as shown in the example below.
People can make a two-digit number using the numbers shown on the spinners using the following rule:
Multiply the number on the first spinner by 10 and then add the number on the second spinner.
One example, as shown above, makes the number 21, because 2 × 10 + 1 = 21.
(a) How many different numbers can be made playing this game? [1]
(b) Write down all the prime numbers that can be made playing this game. [2]
(c) What is the probability that a person makes a prime number when playing the game once? [2]
(d) Sara charges each person £1 to play the game once.
Each player who makes a prime number from their spins wins £2.
How much profit would the school expect to make when 180 people play the game? [4]
Each player who makes a prime number from their spins wins £2.
How much profit would the school expect to make when 180 people play the game? [4]
| Scheme | Marks | Comments |
|---|---|---|
| 9 | B1 | Allow a list of all 9 numbers (no repeats or extras). |
| Scheme | Marks | Comments |
|---|---|---|
| 11, 13, 23, 31. | B2 | All correct with no incorrect numbers. B1 for all correct with at most 2 incorrect. B1 for three correct and at most 1 incorrect. B1 for two correct and 0 incorrect. |
| Scheme | Marks | Comments |
|---|---|---|
| 4/9 ISW | B2 | Correct answer OR F.T. ‘their number of primes’ / ‘their (a)’, provided the resulting fraction is between 0 and 1. B1 4/x with x>4 OR y/9 with y<9 or equivalent for FT Penalise -1 if incorrect notation used e.g. ‘4 out of 9’ |
| Scheme | Marks | Comments |
|---|---|---|
| (Number of winners =) \(\dfrac{4}{9}\) × 180 | M1 | F.T. ‘their 4/9’ if less than 1. M0 for ‘4/9 of 180’ unless correct evaluation shown. |
| = 80 | A1 | A0 if incorrect reduction in (c) is used. |
| (Expected profit =) (£)180 – 80 × (£)2 | M1 | F.T. ‘their stated 80’. |
| = (£)20 | A1 | If the FT results in a loss then ‘Loss’ must be stated or the answer left as a negative. |