Basic Probability: WJEC GCSE Intermediate November 2017 Unit 1 Q6

Intermediate November 2017 Unit 1 Q6

WJECIntermediateCurrent spec9 marksBasic Probability Properties of Numbers

6. Sara is in charge of a game at her school’s Christmas party.

Two fair spinners are spun as shown in the example below.

1st Spinner and 2nd Spinner, each with sections 1, 2, 3. The 1st spinner points to 2 and the 2nd spinner points to 1.

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]

(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]

Mark scheme (a)

Scheme	Marks	Comments
9	B1	Allow a list of all 9 numbers (no repeats or extras).

Mark scheme (b)

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.

Mark scheme (c)

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’

Mark scheme (d)

Scheme	Marks	Comments
(Number of winners =) \(\dfrac{4}{9} \times 180\)	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.