A factory produces a large batch of glass beads, of which 8% are found to have minor surface imperfections. A random sample of 50 beads is selected and the number of imperfect beads is recorded.
Find the probability that there are at most 5 imperfect beads in this sample.
A second random sample of 50 beads is selected and the number of imperfect beads is recorded.
Using a Poisson approximation, estimate the probability that the total number of imperfect beads in the combined sample of size 100 is fewer than 11.
67 exam-style questions on OCR (MEI) A Level Maths 2.4.13 Model with probability distributions. Each one has a worked solution and a mark scheme showing where the marks go.