What is the probability of a sure event?

Question

What is the probability of a sure event?

1. A. 1 (Correct answer)
2. B. 0.5
3. C. 0
4. D. 0.25

Correct Answer

Option A — 1

Detailed Solution & Explanation

The correct answer is 1.

Key Points

• A sure event (or certain event) is one that is guaranteed to occur — its favourable outcomes are the entire sample space.
• $P(\text{sure event}) = \frac{n(S)}{n(S)} = 1$
• Example: getting a number less than 7 when rolling a standard die — every one of the six faces satisfies the condition.

Additional Information

• The probability scale:
  • $0 \leq P(E) \leq 1 \text{ for every event } E$
  • $P(E) = 0$ → impossible event, which can never occur.
  • $P(E) = 1$ → sure event, which must occur.
  • $P(E) + P(\bar{E}) = 1$ — an event and its complement always sum to 1.
• A probability can never be negative or greater than 1; if a calculation produces either, there is an arithmetic error.