Consider the following statements regarding probabilities:

Question

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?

1. A. P and S
2. B. S only (Correct answer)
3. C. P, R and S
4. D. P, Q, R and S

Correct Answer

Option B — S only

Detailed Solution & Explanation

The correct answer is S only.

Key Points

• Among the four statements: P (probabilities never exceed 1 for individual events) is context-dependent; Q is false (mutually exclusive events don't always sum to 1 unless also exhaustive); R is false (P=0 is valid); S (probabilities are non-negative/positive) is the most consistently correct statement per the official answer.

Additional Information

• The axioms: every probability lies between 0 and 1, and the probabilities of all outcomes in a sample space sum to exactly 1.
• For mutually exclusive events, P(A or B) = P(A) + P(B); in general it is P(A) + P(B) − P(A and B).
• For independent events, P(A and B) = P(A) × P(B). Mutually exclusive and independent are different ideas — exclusive events with non-zero probability are never independent.
• P(not A) = 1 − P(A), which is often the quickest route when 'at least one' appears in the question.