A six-faced fair dice is shown until 1 comes. Then the probability that 1 comes in even number of trials is

In single throw of a dice, probability of getting 1 is 1/6 and probability of not getting 1 is 5/6.Then, getting 1 in even number of chances is getting 1 in 2ndchance or in 4th chance or in 6th chance and so on. Therefore, the required probability is56×16+563×16+565×16+⋯+∞=53611−2536=536×3611=511