Question

MATH1234 has an enrolment of 60 students. The lecturer, Brooke Malcolm, will randomly assign 20 students to each of three tutorials A, B and C Friends Xing, Yuxi and Ziyi want to know the probability that at least one of them will end up in tutorial A. The sample space for the 'experiment' of Brooke's choice is the set S of all possible class lists (unordered) for Tutorial A, and the event E of interest is that the outcome of the experiment has non-empty intersection with {X, Y,Z) With the help of WolframAlpha, or some similar computaional aide, for each of the items below find the 2-digit (natural) number that provides the best approximation 14 x 10 14 (b) El (c) P(E) A~ The remaining questions may require more thought and may require the use of some probability rules Using similar methods to those used above find the probabilities below, again giving the 2-digit (natural) number that provides the best approximation (d) The probability that the three friends end up in the same tutorial is approximately %. Hint: First find the probability that they all end up in tutorial A. e) The probability that at least one of the friends ends up in tutorial A, or at least one of the friends ends up in tutorial B, (or both) is approximately (f) [Challenge!l The probability that the three friends end up in three different tutorials is approximately Hint for (f): One method uses this: For any three events E, F, G

Answer 1

2o 42 42 e) P (ot least ens endubicA ore in oria bath) A: ad least onc end ubin A -(mo oni Aoia) all tnc) 5742 494% ber 59158 357C 57 C20 x 20 2