You are rolling a pair of balanced dice in a board game. rolls are independent. you land in a danger zone that requires you to roll doubles (both faces show the same number of spots) before you are allowed to play again. (a) what is the probability of rolling doubles on a single toss of the dice? 25362536 536536 136136 1616 (b) what is the probability that you do not roll doubles on the first toss, but you do on the second toss? 536536 136136 636636 236236 (c) what is the probability that the first two tosses are not doubles and the third toss is doubles? this is the probability that the first doubles occurs on the third toss. 1021610216 2021620216 2521625216 52165216 (d) now you see the pattern. what is the probability that the first doubles occurs on the fourth toss? on the fifth toss? give the general result, that is, what is the probability that the first doubles occurs on the th toss? (56)(−1(56)(16)k−1 −1)(56)(16)(k−1)(56)(16) (−1(16)(56)k−1(16) −1)(−1(16)(k−1)(56)k−1(16) (e) what is the probability that you get to go again within three turns? (enter your answer rounded to four decimal places.) probability: