A cereal manufacturer includes a collectible card in some of its cereal boxes. For a specific promotion, a card is placed in 30% of the boxes. No box contains more than 1 card. The boxes are sold in multipacks of 8 boxes.
(i) Write down a suitable distribution to model the number of cards found in a multipack. (ii) Write down one assumption required for the model.
Find the probability that in 2 randomly selected multipacks, exactly 1 multipack contains exactly 2 cards.
Find the probability that a randomly selected multipack contains at least 3 cards.
An organizer buys 100 multipacks for a school event.
Using a normal approximation, find the probability that more than 40 of these multipacks contain at least 3 cards.
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.