6. A "level-passing game" stipulates: On the $n$-th level, a die must be rolled $n$ times. If the sum of the points that appear in these $n$ rolls is greater than $\frac{3^{n}}{4}$, it counts as passing the level; otherwise, it does not count as passing. (Note: The die is a uniform cube with the numbers $1, 2, 3, 4, 5, 6$ marked on its faces. When the die is thrown and comes to rest, the number on the top face is the number that appears.) There are the following statements:
(1) Passing the first level is a certain event,
(2) It is possible to pass the fourth level,
(3) The probability of passing the fifth level is greater than 0,
(4) The probability of passing the second level is $\frac{35}{36}$.
Among these, the number of correct statements is ( ).
(A) 4
(B) 3
(C) 2
(D) 1
6.B.

To pass the first level, the score must be greater than $\frac{3}{4}$. Clearly, rolling a die once yields at least 1 point. Therefore, (1) is correct.

Since $4 \times 6=24, \frac{3^{4}}{4}=20 \frac{1}{4}, 24>20 \frac{1}{4}$, the fourth level can be passed. Therefore, (2) is correct.

Since $5 \times 6=30, \frac{3^{5}}{4}=60 \frac{3}{4}, 30<60 \frac{3}{4}$, passing the fifth level is an impossible event, with a probability of 0. Therefore, statement (3) is incorrect.

To pass the second level, the sum of the scores must be greater than $\frac{9}{4}$, which means the sum of the scores must be at least 3. When rolling twice, the minimum sum is 2, so the only way not to pass the second level is if both rolls result in 1. Out of the 36 possible outcomes of rolling twice, 35 outcomes can pass the second level. Therefore, the probability of passing the second level is $\frac{35}{36}$. Hence, (4) is correct.