Grade 12 Maths · Probability · Paper 1

Counting Principle Grade 12

Real Counting Principle past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 14 past paper questions
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Question 10.2 · May/June 2025 · Paper 1 · National (DBE) · 6 marks

10.2 A game at a fun park requires a player to roll a six-sided dice and pick a card from a deck of 52 cards. A player wins if an odd number appears on the uppermost face of the dice and the player also draws a picture card from the deck. A deck of cards has 4 suites (hearts, diamonds, spades and clubs). There are 4 picture cards (king, queen, jack and ace) in every suite. A player pays R10 to play a game and in an hour, 260 people can each play one game. If the owner wants to make a 70% profit per hour, calculate the maximum amount that the owner must pay out to each winner.(6)

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4. Question 12.1 · November 2024 · Paper 1 · National (DBE) · 2 marks
A company generates a 4-character code using the 26 letters of the alphabet and the 10 digits, from 0 to 9. The code is in the form: Letter Digit Letter Digit.
12.1 Determine how many different codes can be formed if letters and digits may be repeated.(2)
Show the memo (1 tick)Memo
1. ✓
  Apply fundamental counting principle $26 \times 10 \times 26 \times 10 = 67600$
  2 marks · Use the counting principle
5. Question 11.3.2 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
11.3 Seven guitar players, each with a different name, participate in a concert.
11.3.2 After the performance, the guitar players wait backstage. There is a bench with only room for four to sit on. What will be the probability that the four guitar players will be sitting in alphabetical order, from left to right?(3)
Show the memo (2 ticks)Memo
1. ✓
  Calculate total sample space for arranging 4 from 7 $7 \times 6 \times 5 \times 4 = 840$
  2 marks · Use the counting principle
2. ✓
  Calculate probability for the single successful arrangement $P = \frac{1}{840}$
  1 mark · Calculate a simple probability
6. Question 12.1.1 · September 2024 · Paper 1 · Provincial · 3 marks
12.1 The data obtained from a city's police department indicates that of all motor vehicles reported stolen, 80% were stolen by syndicates to be sold off, and 20% were stolen by individuals for personal use. Of the vehicles presumed stolen by syndicates: 24% were recovered within 48 hours, 16% were recovered after 48 hours, 60% were never recovered. Of those vehicles presumed stolen by individuals: 38% were recovered within 48 hours, 58% were recovered after 48 hours, 4% were never recovered.
12.1.1 Draw a tree diagram for the given information above.(3)
Show the memo (3 ticks)Memo
1. ✓
  First levelSyndicate (0.8) / Individual (0.2)
  1 mark · Draw a tree diagram
2. ✓
  Second level S0.24, 0.16, 0.60
  1 mark · Draw a tree diagram
3. ✓
  Second level I0.38, 0.58, 0.04
  1 mark · Draw a tree diagram

Counting Principle Grade 12 videos

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Math Antics - Basic Probabilitymathantics

Grade 12 Fundamental Counting Principle Permutations with restrictions (NSC Maths\DBE\CAPS ) | NTENTE \ New Technological Education

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