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0580/33 May/Jun 2024, Question 7: Basic Probability

Cambridge IGCSE Mathematics 0580 · Paper 33 (Core) · Calculator · 12 marks

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The question, in short

Probability questions: spinner outcomes, drawing on a scale, a bag of red and green balls, two 4-sided spinners multiplied, and a replacement tree diagram for red and blue discs.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 1 mark

Mark an arrow on the 0 to 1 probability scale for the spinner landing on 2.

  1. 1P(2) = 1/6: draw the arrow at the first of the six divisions after 0

AnswerArrow at 1/6

Part (aii) · 1 mark

Find the probability the 6-sided spinner lands on a prime number.

  1. 1Primes on the spinner: 2, 3, 5
  2. 2P(prime) = 3/6 = 1/2

Answer1/2

Part (aiii) · 1 mark

Find the probability the spinner lands on the number 7.

  1. 1There is no 7 on the spinner: probability = 0

Answer0

Part (b) · 2 marks

Find the probability a random ball from 3 red and 12 green is green, as a simplified fraction.

  1. 1P(green) = 12/(3 + 12) = 12/15
  2. 2= 4/5

Answer4/5

Part (ci) · 1 mark

Using the multiplication table for two 4-sided spinners, find the probability the score is even.

  1. 1Odd scores need both numbers odd: 4 of the 16 outcomes
  2. 2P(even) = 12/16 = 3/4

Answer3/4

Part (cii) · 1 mark

Using the table, find the probability the score is an integer.

  1. 1Every score is an integer: 16/16 = 1

Answer1

Part (ciii) · 1 mark

Using the table, find the probability the score is at least 10.

  1. 1Scores of at least 10: 12, 12, 16
  2. 2P = 3/16

Answer3/16

Part (di) · 2 marks

Complete the tree diagram for two picks with replacement, given red probability 1/5.

  1. 1P(blue) = 1 − 1/5 = 4/5
  2. 2The disc is replaced, so every Red branch is 1/5 and every Blue branch is 4/5

AnswerFirst disc: Red 1/5, Blue 4/5 Second disc after Red: Red 1/5, Blue 4/5 Second disc after Blue: Red 1/5, Blue 4/5

Part (dii) · 2 marks

Work out the probability that both discs picked are blue.

  1. 1P(blue, blue) = 4/5 × 4/5
  2. 2= 16/25

Answer16/25

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