A box contains n n\,n petrol key fobs and 6 diesel key fobs, where n n\,n is a positive integer. Two fobs are taken from the box at random, without replacement.
The probability that both fobs taken are diesel is 18\displaystyle \frac{1}{8}81.
Show that n2+11n−210=0n^2 + 11n - 210 = 0n2+11n−210=0.
Hence find the value of nnn.
Find the probability that the two fobs taken are of different types.
198 exam-style questions on AQA A Level Maths 2.3 M: Probability, covering 2.3.1 Mutually exclusive and independent events, 2.3.2 Conditional probability (A-level only), 2.3.3 Modelling with probability (A-level only), and 2.3 M: Probability. Each one has a worked solution and a mark scheme showing where the marks go.