Which of the following cannot be the probability of an event? (A) 2 3 (B) –1.5 (C) 15% (D) 0.7
Step-by-Step Solution
Key Concept: For any event, its probability $P$ must satisfy $0 \le P \le 1$. Values outside this interval cannot represent a probability.
1. Write down the fundamental property of probability:
$$0 \leq P(E) \leq 1$$
2. Convert each option to a decimal (if needed) and compare with the interval.
- (A) $\frac{2}{3}=0.666\ldots$ → lies between 0 and 1 → valid.
- (B) $-1.5$ → less than 0 → invalid.
- (C) $15\% = 0.15$ → lies between 0 and 1 → valid.
- (D) $0.7$ → lies between 0 and 1 → valid.
3. The only option that violates the condition $0 \le P \le 1$ is (B).
4. Hence, (B) cannot be the probability of an event.
Correct Answer: (B) –1.5