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A student writes her safety & dependability exam, and nishes after

one hour. Slightly bored, she starts ipping three perfe t oins (two sides, heads and tails,

equal probability). In every throw, she ounts the number of heads (whi h is between 0

and 3), and, starting with the value 1, writes down the value of the produ t of the results

(#heads in the respe tive ast) seen so far modulo 4.

(A series 3, 1, 3, 2, 3, 0, . . . of results, for example, would be translated to

1, 3, 3 1, 2, 2, 0, . . . , where the rst 1 is the value she started with.)

(a) Model her exam pastime as a dis rete time Markov hain. (8 marks)

(b) Determine the probability that she writes down odd values until she writes down the

value 2. (10 marks)

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