Example 1: In a "level-passing game", the rule is: 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 $\frac{3^{n}}{4}$, then it is considered passing the level; otherwise, it is not considered passing. There are the following statements:
(1) Passing the first level is a certain event;
(2) The probability of passing the second level is $\frac{35}{36}$;
(3) It is possible to pass the fourth level;
(4) The probability of passing the fifth level is greater than zero.
Among them, the number of correct statements is ( ).
(A) 4
(B) 3
(C) 2
(D) 1
Explanation: To pass the first level, the score needs to be greater than $\frac{3}{4}$. Clearly, rolling a die once will yield at least one point, so (1) is correct.

To pass the second level, the sum of the scores needs to be greater than $\frac{9}{4}$, which means the sum of the scores must be at least 3. Since the sum of the scores from two rolls is at least 2, the only way to fail the second level is if both rolls result in 1. Out of the 36 possible outcomes from two rolls, 35 outcomes can pass the second level. Therefore, the probability of passing the second level is $\frac{35}{36}$. So (2) is correct.

To pass the fourth level, the sum of the scores needs to be greater than $\frac{3^{4}}{4} = 20 \frac{1}{4}$. If each roll results in 6, the sum of the scores will be 24, which is greater than $20 \frac{1}{4}$. Therefore, the fourth level can be passed. So (3) is correct.

To pass the fifth level, the sum of the scores needs to be greater than $\frac{3^{5}}{4}$. Clearly, this is impossible, so passing the fifth level is an impossible event with a probability of 0. So (4) is incorrect.

Note: This question is a basic problem about probability concepts, and the key is to correctly understand the meaning of passing the levels.