A botanical garden offers a "rare bloom" seed in 15% of its wildflower packets. No packet contains more than one rare bloom seed. Packets are sold in wholesale bundles of 12.
(i) Suggest a suitable distribution to model the number of rare bloom seeds, SSS, found in a single bundle. (ii) State one necessary assumption for this model to be valid.
Calculate the probability that out of 3 randomly selected bundles, exactly 1 bundle contains exactly 2 rare bloom seeds.
Determine the probability that a randomly selected bundle contains at least 3 rare bloom seeds.
A regional distributor buys 120 bundles for a seasonal sale.
Using a normal approximation, find the probability that fewer than 25 of these bundles contain at least 3 rare bloom seeds.
390 exam-style questions on OCR (MEI) A Level Maths 2.4 Probability Distributions, covering 2.4.1 Recognise binomial situations, 2.4.2 Probability of success p, 2.4.3 Calculate binomial probabilities, 2.4.4 Mean of the binomial distribution, 2.4.5 Expected frequencies for binomial, 2.4.6 Probability functions and discrete random variables, 2.4.7 Numerical probabilities for a simple distribution, 2.4.8 Normal distribution as a model (A-level only), 2.4.9 Shape of the Normal curve (A-level only), 2.4.10 Linear transformation and standardising (A-level only), 2.4.11 Symmetry and inflection of Normal curve (A-level only), 2.4.12 Calculate probabilities from a Normal distribution (A-level only), 2.4.13 Model with probability distributions, and 2.4 Probability Distributions. Each one has a worked solution and a mark scheme showing where the marks go.