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### Question

An experiment consists of flippingan unfair coin and spinning an unusual roulette wheel. For the coin it is known that the probablyof heads is35. The roulette wheel consists of 16 sectors, that are numbered from 1 to 16 in order.Sectors 1,5,9,13 are red, sectors 2,6,10,14 are green, sectors 3,7,11,15 are black and sectors 4,8,12,16are white. Assume that each sector on the roulette is equally likely to occur.The set of all possible outcomes of this experimentcan be defined as follows:Ω ={h1, t1, h2, t2, h3, t3, ..., h16, t16},where for example the outcome ’h4’ means that the coin shows heads and the roulette result is 4.Considered are the following events:Ais the event that the coin shows either tails or heads and the roulette result is a green sector.Bis the event that the coin shows heads and the the roulette result is a number which is multipleof 5.Cis the event that the coin shows tails and the the roulette result is a number greater than 6and smaller than 15.Dis the event that the coin shows either heads or tails and the roulette result is either multipleof 3 or a number greater than 11.Now do the following(a) Determine the probabilities of each possible outcome of the experiment, i.e. determineP({hi})andP({ti}), wherei= 1,2, ...,16(b) Define eventsA,B,CandDas subsets ofand find the probabilities of each eventA,B,CandD.(c) Using the definition of two independent events, decide ifA,B,C,Dare pairwise independent?( Hint: there are 6 different pair combinations for these events. To answer this question, checkif the definition of independent events is satisfied for each pair.)(d) Decide ifA,CandDare mutually independent. Justify your answer.(e) Decide if theA,B,CandDare mutually independent. Justify your answer

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