An archaeologist, Dr. Aris, is examining a collection of ancient pottery shards recovered from a site. For each shard found in the upper strata, independently of all others, the probability that it possesses a specific geometric decoration is 0.35.
Find the probability that, in a random sample of 10 shards from the upper strata, the number of shards with geometric decorations is
exactly 4,
at most 2.
Dr. Aris then excavates a deeper, high-density layer. In this layer, the probability that any shard possesses the geometric decoration, independently of all others, is 0.4.
A hoard of 150 shards is recovered from this deeper layer.
Calculate the mean and the variance for the number of shards in this hoard of 150 that possess geometric decorations.
Using a suitable approximation, determine the probability that more than 70 of these shards possess geometric decorations.
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.