Grade 10 Maths · Probability · Calculate a simple probability

Theoretical Probability Grade 10

List all possible outcomes and find a probability as favourable outcomes over total outcomes (for example rolling a 6 on a die is 1/6).

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Question 11.2 · May/June 2025 · Paper 1 · National (DBE) · 3 marks

Consider the three-digit numbers from 501 up to 999.

11.2 Calculate the probability of a three-digit number not satisfying the condition given in QUESTION 11.1.(3)

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More past paper questions: calculate a simple probability

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3. 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
4. Question 9.2.3 · November 2023 · Paper 1 · Provincial · 3 marks
9.2 A cellphone distribution company investigated the number of defective phones that they obtain from two suppliers, Axis Phones and Direct Phones. They recorded their findings in a contingency table, shown below.

Answer the questions that follow. $Diagram for question 9.2$
9.2.3 Calculate the probability that a cellphone chosen at random is Not Defective OR it is from Axis Phones and Defective.(3)
Show the memo (3 ticks)Memo
1. ✓
  $\frac{514}{600}$ P(not defective) + P(Axis Phones and defective)
  $= \frac{514}{600}$
  1 mark · Calculate a simple probability
2. ✓
  $+ \frac{58}{600}$ $+ \frac{58}{600}$
  1 mark · Use the addition rule
3. ✓
  Answer $= \frac{572}{600} = \frac{143}{150}$ or $0, 95$
  1 mark · Use the addition rule
5. Question 9.2.2 · November 2025 · Paper 1 · Provincial · 4 marks
9.2 The contingency table below represents 106 athletes' responses regarding jogging on the sand.

Answer the questions that follow. $Diagram for question 9.2$
9.2.2 Is the event "enjoy jogging on sand" independent of the gender?(4)
Show the memo (4 ticks)Memo
1. ✓
  P(Enjoy jogging) $\times$ P(Male)P(Enjoy jogging) $= \frac{56}{106}$ ; P(Male) $= \frac{42}{106}$
  P(Enjoy jogging) $\times$ P(Male) $= \frac{56}{106} \times \frac{42}{106}$
  1 mark · Use the product rule for independence
2. ✓
  Answer $= 0, 20932...$
  1 mark · Use the product rule for independence
3. ✓
  P(Enjoy jogging and Male)P(Enjoy jogging and Male) $= \frac{26}{106} = 0, 24528...$
  1 mark · Calculate a simple probability
4. ✓
  ConclusionP(Enjoy jogging and Male) $\neq =$ P(Enjoy jogging) $\times$ P(Male)
  $∴$ Events are not independent.
  1 mark · Use the product rule for independence
6. Question d · Siyavula Grade 8 Mathematics, 26 Probability, Relative frequency, Worked example 26.4 · 1 mark
We toss a coin $20$ times and observe the outcomes. The results of the trials are listed below.
$H; H; H; T; T; H; H; H; H; H; T; T; H; T; T; H; T; T; T; H$
d Calculate the theoretical probability of observing heads.(1)
Show the memo (1 tick)Memo
1. ✓
  Theoretical probabilityThere are two possible outcomes, heads or tails, so $n (S) = 2$ . $E = {H}$ , so $n (E) = 1$ .
  $P (E) = \frac{n ( E )}{n ( S )} = \frac{1}{2} = 0, 5$
  1 mark · Calculate a simple probability

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