Which of the following cannot be the probability of an event?

Question

Accepted Answer

The correct option is 1:
To solve this problem, we need to recall the fundamental properties of probability. The probability of any event, let's denote it as $P(E)$, must always satisfy the following condition:
$$0 \le P(E) \le 1$$
This means that the probability of an event can be any value from 0 to 1, inclusive.  * A probability of 0 indicates an impossible event (it will never happen).
  * A probability of 1 indicates a sure or certain event (it will always happen).
  * Probabilities between 0 and 1 represent the likelihood of an event occurring.Let's examine each of the given options:1.  **-1.5**: This value is less than 0. According to the properties of probability, a probability cannot be a negative number. Therefore, -1.5 cannot be the probability of an event.

2.  **$\frac{2}{3}$**: To check if this is a valid probability, we convert it to a decimal: $\frac{2}{3} \approx 0.666...$. This value is between 0 and 1 ($0 \le 0.666... \le 1$). Thus, $\frac{2}{3}$ can be the probability of an event.

3.  **15%**: To convert a percentage to a decimal, we divide by 100: $15% = \frac{15}{100} = 0.15$. This value is between 0 and 1 ($0 \le 0.15 \le 1$). Thus, 15% can be the probability of an event.

4.  **0.7**: This value is directly given as a decimal and is between 0 and 1 ($0 \le 0.7 \le 1$). Thus, 0.7 can be the probability of an event.From our analysis, only -1.5 violates the fundamental rule that probability must be non-negative.

The incorrect option is 2: $\frac{2}{3}$ is incorrect because $\frac{2}{3}$ is approximately 0.67, which is a value between 0 and 1, and therefore can be a probability.
The incorrect option is 3: 15% is incorrect because 15% is equivalent to 0.15, which is a value between 0 and 1, and therefore can be a probability.
The incorrect option is 4: 0.7 is incorrect because 0.7 is a value between 0 and 1, and therefore can be a probability.