Practice · Maths AA SL · 2021 syllabus · 4.8
IB Maths AA SL 4.8 The binomial distribution: practice questions
2 exam-style questions on 4.8 The binomial distribution, SL: 1 Paper 2 short and 1 Paper 2 long. Each one comes with the mark scheme, a model answer and the reasoning behind every mark. Free with an account.
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4.8-02 · Paper 2 style · Section A · calculator · 7 marks
Tulip bulbs from two growers
A florist buys tulip bulbs from two growers. 8% of the bulbs from Hansen Farm fail to flower, and 18% of the bulbs from Okafor Gardens fail to flower. Each order is a box of 12 bulbs, all from one grower. An order comes from Hansen Farm with probability 0.7 and from Okafor Gardens with probability 0.3. Whether a bulb flowers is independent of the other bulbs in the box.
(a) Find the probability that exactly 2 bulbs in an order fail to flower. [4]
(b) Given that exactly 2 bulbs in an order fail to flower, find the probability that the order came from Okafor Gardens. [3]
Show the answer and the reasoning
(a) Mark scheme
- (M1) recognising a binomial distribution, e.g. \(\binom{12}{2}p^2(1 - p)^{10}\) OR \(\mathrm{B}(12, p)\);
- (M1) considering both growers, with \(p = 0.08\) and \(p = 0.18\);
- (A1) \(0.7 \times 0.183485... + 0.3 \times 0.293918...\);
- A1 0.217 (0.216615...);
A model answer: Let \(F\) be the number of bulbs that fail. Hansen Farm: \(F \sim \mathrm{B}(12, 0.08)\) and \(P(F = 2) = 0.183485...\). Okafor Gardens: \(F \sim \mathrm{B}(12, 0.18)\) and \(P(F = 2) = 0.293918...\). Total: \(0.7 \times 0.183485... + 0.3 \times 0.293918... = 0.217\) (0.216615...).
(b) Mark scheme
- (M1) recognising conditional probability in context: \(\frac{P(\text{Okafor and 2 fail})}{P(\text{2 fail})}\);
- (A1) \(\frac{0.3 \times 0.293918...}{0.216615...}\) OR \(\frac{0.0881756...}{0.216615...}\);
- A1 0.407 (0.407060...);
A model answer: \(P(\text{Okafor} \mid \text{2 fail}) = \frac{0.3 \times 0.293918...}{0.216615...} = \frac{0.0881756...}{0.216615...} = 0.407\) (0.407060...).
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The 2 questions in 4.8
- 4.8-01 Visitors at two science shows
- 4.8-02 Tulip bulbs from two growers
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Every Maths question here is original, each one modelled on a question from the AI SL or AA SL papers set since 2021, with a new context and new numbers. Developed independently from the International Baccalaureate Organization, which has not endorsed it. Found a mistake? Email vytis@limeadmissions.com with the question id.