CIE iGCSE Maths C8.1 Introduction to probability Exam Style Practice Questions- Paper 1
▶️ Answer/Explanation
(b) To find the probability of both being faulty, we follow the “Faulty” branch for the first battery and multiply it by the “Faulty” branch for the second: $\frac{1}{10} \times \frac{1}{10} = \frac{1}{100}$.
(c) The expected value is found by multiplying the total number of items by the probability of the event occurring: $3000 \times \frac{1}{10} = 300$.
✅ Answer:
(a) Missing probabilities are $\frac{9}{10}$ and $\frac{1}{10}$ filled in appropriately
(b) $\frac{1}{100}$
(c) 300
▶️ Answer/Explanation
(a)
Even numbers from 1–8 are \(\{2, 4, 6, 8\}\), so 4 out of 8 discs are even: \(P(\text{even}) = \dfrac{4}{8} = \dfrac{1}{2} = 0.5\).
✅ Arrow A placed at \(0.5\) (the midpoint of the scale)
(b)
There is no disc numbered 9 in the bag (discs go from 1 to 8 only), so it is impossible: \(P(9) = 0\).
✅ Arrow B placed at \(0\) (the left end of the scale)
(c)
Numbers less than 3 from 1–8 are \(\{1, 2\}\), giving 2 out of 8 discs: \(P(\text{less than } 3) = \dfrac{2}{8} = \dfrac{1}{4} = 0.25\).
✅ Arrow C placed at \(0.25\) (one quarter of the way along the scale)
▶️ Answer/Explanation
(a)(i) \(\frac{3}{8}\)
(a)(ii) 1
(b) 60
(a)(i) Probability of landing on 7: There are 3 sevens out of 8 possible outcomes → \(\frac{3}{8}\).
(a)(ii) All numbers (3,4,7,8,9) are >2 → Probability = \(\frac{8}{8} = 1\).
(b) Expected number of 7’s in 160 spins: \(160 \times \frac{3}{8} = 60\).