Final answer:
The probability that a person first wins on their sixth ticket is given by (0.65)^5 * (0.35), which is the formula for a geometric distribution, considering five losses followed by one win.
Step-by-step explanation:
To calculate the probability that a person first wins on their sixth scratch-off lottery ticket, we have to account for five losses followed by one win. The probability that she loses a ticket is 1 - 0.35 = 0.65. Therefore, for the person to lose the first five tickets and then win on the sixth, we use the formula for a geometric distribution which is given by (probability of failure)^(number of failures) * (probability of success).
Applying this to the scenario, the probability of losing the first five is (0.65)^5, and the probability of then winning on the sixth ticket is 0.35. So, the probability that she first wins on the sixth ticket is (0.65)^5 * (0.35). Furthermore, since order matters and there is only one specific sequence of loss-loss-loss-loss-loss-win, we do not need to multiply by any combinations or permutations.
Therefore, the correct answer would be (0.65)^5 * (0.35), which is not explicitly listed in the options provided. However, if the intention was to include the combination of choosing 1 win out of 6 tickets, then the complete calculation would be: 6C1 * (0.65)^5 * (0.35), where '6C1' indicates the number of ways to arrange one win in six trials. So the correct answer would be an adjusted version of option D, which could be a typo in the given options.