Basic Probability: WJEC GCSE Higher November 2024 Unit 2 Q7

Higher November 2024 Unit 2 Q7

WJECHigherCurrent spec5 marksBasic Probability

7. PowrUp is a company that makes batteries.
The quality of the batteries is tested regularly.
PowrUp calculates the relative frequency of faulty batteries after checking a total of 1000, 2000, 3000, 4000 and 5000 batteries.
The results are plotted on the graph below.

Graph of relative frequency (0 to 0·05) against number of batteries (0 to 5000) with five plotted points: 1000, 0·030; 2000, 0·027; 3000, 0·033; 4000, 0·029; 5000, 0·032

(a) One battery is selected at random.
Write down the best estimate for the probability that this battery will be faulty.
You must give a reason for your choice. [2]

Probability = …………

Reason:

(b) It costs the company 2·6p to dispose of each of the faulty batteries.
How much will it cost the company to dispose of all the faulty batteries after testing the first 3000 batteries?
You must show all your working. [3]

Mark scheme (a)

Scheme	Marks	Comments
Sight of 0·032 or equivalent e.g. 3·2% or \(\frac{160}{5000}\)	B1	Answer line takes precedence. ISW. Allow incorrect probability notation e.g. 160 out of 5000.
Explanation e.g. ‘all data used’, ‘last point plotted’, ‘the number of batteries checked was the highest’.	E1	Accept any indication that the final reading should give the best estimate. Allow ‘the more times you repeat an action, the more accurate the estimate is’.

Mark scheme (b)

Scheme

Marks

Comments

May be done in any order.

3000 × 0·033 × 0.026 or 3000 × 0·033 × 2.6

May be seen in stages or implied in later working.
Award M1 for sight of one of the following, allowing one place value error in 0·033 or 0.026 (may be embedded):

3000 × 0·033
99
3000 × (£)0.026
3000 × 2.6(p)
(£)78 or 7800(p)
0.026 × 0·033
2.6 × 0·033
0·000858
0·0858.

Award M1 for sight of the consecutive digits 99 or 78 or 858 in a number involving a place value error e.g. 990 but not 8990.

(£)2.57(4) or 257(.4)(p) ISW

CAO.
Allow (£)2.58 or 258(p) (If units are given they must be correct).
Incorrect units may imply M2 A0.

Award M1 A0 for one of the following answers:

Answer	From
2(.)34	(3000 × 0.026 × 0·03)
2(.)10(6) or 2(.)11	(3000 × 0.026 × 0·027)
2(.)26(2)	(3000 × 0.026 × 0·029)
2(.)49(6) or 2(.)50	(3000 × 0.026 × 0·032)

Corrected by Westie's Workshop

The board's mark scheme printed “2(.)62(2)”. Changed to “2(.)26(2)” because 3000 × 0.026 × 0·029 = 2.262, so the answer is 2(.)26(2), not 2(.)62(2).

Original: see the board's mark scheme PDF (link above).