The probability that a circuit board fails an electrical inspection is 0.18, independently of every other circuit board. A random sample of n n\,n circuit boards is inspected.
Show that the probability that at least one of the n n\,n cars fails is 1−0.82n1 - 0.82^n1−0.82n.
Find the smallest value of n n\,n for which this probability exceeds 0.99.
State one assumption needed for the binomial model to be appropriate here.
390 exam-style questions on OCR A Level Maths 2.4 Statistical Distributions, covering 2.4.1 Discrete probability distributions, 2.4.2 Binomial distribution as a model, 2.4.3 Calculating binomial probabilities, 2.4.4 Mean and variance of the binomial (A-level only), 2.4.5 Normal distribution as a model (A-level only), 2.4.6 Probabilities using the normal distribution (A-level only), 2.4.7 Links to histograms, mean and standard deviation (A-level only), and 2.4.8 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.