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0580/31 May/Jun 2023, Question 9: Basic Probability

Cambridge IGCSE Mathematics 0580 · Paper 31 (Core) · Calculator · 6 marks

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The question, in short

Use a fair 7-sided spinner numbered 1 to 7 to justify a probability of 4/7, complete a two-spin tree diagram, and find the probability of prime on both spins.

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

Part (a) · 2 marks

Explain why landing on a prime number has probability 4/7 for the 1 to 7 spinner.

  1. 1The prime numbers from 1 to 7 are 2, 3, 5 and 7 (1 is not prime), so 4 prime outcomes
  2. 2There are 7 equally likely outcomes, so P(prime) = 4/7

AnswerPrimes 2, 3, 5 and 7 and no others in the explanation; there are 7 possible outcomes

Part (bi) · 2 marks

Fill in the missing probabilities on the tree diagram for two spins.

  1. 1P(not prime) = 1 − 4/7 = 3/7
  2. 2The spins are independent, so every 2nd spin branch is the same
  3. 3Prime 4/7, Not prime 3/7 on each pair of branches

Answer1st spin: Prime 4/7, Not prime 3/7 2nd spin after Prime: Prime 4/7, Not prime 3/7 2nd spin after Not prime: Prime 4/7, Not prime 3/7

Part (bii) · 2 marks

Calculate the probability that both spins give a prime number.

  1. 1P(prime, prime) = 4/7 × 4/7
  2. 2= 16/49

Answer16/49

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