A-LevelMathematicsProbability and statisticsFeb/Mar 2022Paper 6 Q710 Marks
(a) Two ponds, A and B, each contain a large number of fish. It is known that 2.4% of fish in pond A are carp and 1.8% of fish in pond B are carp. Random samples of 50 fish from pond A and 60 fish from pond B are selected. Use appropriate Poisson approximations to find the following probabilities. (i) The samples contain at least 2 carp from pond A and at least 2 carp from pond B. (ii) The samples contain at least 4 carp altogether. (b) The random variables X and Y have the distributions Po(λ) and Po(μ) respectively. It is given that • P(X = 0) = [P(Y = 0)]², • P(X = 2) = k[P(Y = 1)]², where k is a non-zero constant. Find the value of k.
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