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...

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