Consider the following statements regarding probabilities:

P: Probabilities can never add up to more than one.

Q: Probabilities of mutually exclusive events always add up to one.

R: Probabilities can never be zero

S: Probabilities are always positive

Which of the following statement is correct?

P is CORRECT: The sum of probabilities for all possible outcomes in a sample space must equal exactly $1$. Therefore, probabilities can never add up to more than $1$.Q is INCORRECT: While probabilities of mutually exclusive events can add up to one (if they are also "exhaustive," meaning they cover all possibilities), they do not always do so. For example, if you roll a six-sided die, the events "rolling a 1" and "rolling a 2" are mutually exclusive, but their probabilities add up to $1/3$, not $1$.R is INCORRECT: A probability can be zero. A probability of $0$ indicates an "impossible event" (e.g., the probability of rolling a $7$ on a standard six-sided die).S is CORRECT: Probabilities are non-negative. They range from $0$ (impossible) to $1$ (certain). In mathematical terms, $0 \leq P(A) \leq 1$.