Consider a dishonest casino that occasionally uses biased dice. The fair die is used 9 times as often as the biased one, with the biased die made so that 6 is rolled with probability 0.18, and the other five numbers are equally likely as each other. Compute the following quantities.
(i) P(6 is rolled)
(ii) P(biased die used — 6 is rolled)
(iii) P(biased die used — 6 not rolled)
(iv) The number of 6's in a row we would need to see before it is more likely that we had been using the biased die
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