6. Among the following statements, the correct option is ( ).
(A) A sample has only one mode.
(B) The median of a sample is always one of the numbers in the sample.
(C) The variance of a sample is always a positive number.
(D) Fans A, B, and C decide who gets the only ticket by drawing lots. They prepare three pieces of paper, one with a star drawn on it and the other two blank, and roll them into three identical-looking paper balls. The person who draws the paper with the star gets the ticket. In this scenario, the chance of drawing the star is the same for the first and the last person to draw.
6.D.

Option (A) is incorrect. For example, the mode of the sample $3,3,5,5,1,2$ has two numbers, 3 and 5.

Option (B) is incorrect. For example, the median of the sample $1,2,3,4$ is $\frac{2+3}{2}=2.5$, and 2.5 is not a data point in the sample.

Option (C) is incorrect. For example, in the sample $80,80,80,80,80$, the variance $S^{2}=0$.

Option (D) is correct. Use the tree diagram shown in Figure 7 to list the results.

From Figure 7, it is found that the probability of the first person drawing is the same as the last person drawing, both being $\frac{1}{3}$.