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. how long will you wait to play again? (assume a standard six-sided die.)
(a) what is the probability of rolling doubles on a single toss of the dice? (enter your probability as a fraction.)
incorrect: your answer is incorrect.
(b) what is the probability that you do not roll doubles on the first toss, but you do on the second toss? (enter your probability as a fraction.)
incorrect: your answer is incorrect.
(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. (enter your probability as a fraction.)
(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: what is the probability that the first double occurs on the kth toss?
(e) what is the probability that you get to go again within two turns? (round your answer to four decimal places.)