The situation described in the question is a typical application of the binomial distribution. The binomial distribution is used when we have a series of independent trials - each trial with a fixed probability of success - and we are interested in the number of successful outcomes we obtain. The key characteristics of a binomial distribution are:
1. The number of trials is fixed beforehand.
2. The trials are independent of one another.
3. There are only two possible outcomes for each trial - success or failure.
4. The probability of success is constant across trials.
Let's look at the situation given in the question:
A fair die is rolled 50 times. Here, rolling the die each time can be considered as a trial. The number of trials (n) is therefore 50.
The trials are independent because the outcome of one roll does not affect the outcome of any other roll.
We have two possible outcomes for each trial: rolling a "6" (success), or not rolling a "6" (failure).
And the probability of success is constant across trials, as the chance of rolling a "6" on a fair six-sided die is always 1/6.
Therefore, we can conclude that the random variable X, representing the number of times a "6" appears in our 50 trials, does indeed follow a binomial distribution, with n = 50 trials.
So, the correct answer is (A): Yes, n = 50.