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Q1: (Pairwise Independent vs. Mutually Independent: 10 marks) Three given events A, B, C are Pairwise Independent, if the following 3 conditions are satisfied: 1) P[AnB] = P[A] P[B] 2) P[AnC] = P[A] P[C] 3) P[COB] = P[C] P[B] Three given events A. B, C are Mutually Independent, if the following 4 conditions are satisfied: 1) P[AnB] = P[A] P[B] 2) P[ANC] = P[A] P[C] 3) P[COB] = P[C] P[B] 4) P[AnBOC] = P[A] P[B] P[C] From the definitions above, we can clear see that mutual independence implies pairwise independence. Show that the converse is not true by using the following example: Throw two fair dice and consider the events: A={the sum of the points is 7}, B={the first die rolled a 3), and C={the second die rolled a 4}.Q2 [10 marks] Randomly select 3 balls from the box below without replacement. n_draws B W W W/O R without replacement Verify the experiment is not a Binomial Experiment. Hint: check the following 4 conditions a) n is pre-determined. b) Only two possible outcomes - Bernoulli trials. c) Identical trials. d) Independent trials