Question

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

• A. $\frac{2}{3}$
• B. -1.5
• C. 20\%
• D. 0.7

Hint:

Remember the golden rule of probability: The probability of any event must be a number between 0 and 1, inclusive. Any value outside this range (i.e., negative or greater than 1) is not a valid probability.

Answer 1

The Correct Option is B

Step 1: Recall the fundamental properties of probability.
The probability of any event, denoted as $P(E)$, must always satisfy two key conditions: (A) Non-negativity: The probability of an event cannot be negative. It must be greater than or equal to 0. So, $P(E) \ge 0$. (B) Upper bound: The probability of an event cannot be greater than 1. It must be less than or equal to 1. So, $P(E) \le 1$. Combining these, the probability of any event $E$ must lie in the range $[0, 1]$, i.e., $0 \le P(E) \le 1$. Step 2: Evaluate each given option against these properties.

(1) $\frac{2{3}$:} This is a fraction. As a decimal, $\frac{2}{3} \approx 0.666...$. This value is clearly between 0 and 1. Therefore, $\frac{2}{3}$ can be the probability of an event.
(2) -1.5: This is a negative number. According to the non-negativity property of probability, a probability value cannot be less than 0. Therefore, -1.5 cannot be the probability of an event.
(3) 20\%: Percentages can be converted to decimal form by dividing by 100. $20\% = \frac{20}{100} = 0.2$. This value is between 0 and 1. Therefore, 20\% can be the probability of an event.
(4) 0.7: This is a decimal number. This value is between 0 and 1. Therefore, 0.7 can be the probability of an event. Step 3: Identify the value that cannot be a probability.
Based on the evaluation, -1.5 is the only option that violates the fundamental rules of probability. $$(2) -1.5$$