Question

Which of the following can not be the probability of an event ?

• A. $\frac{39}{100}$
• B. $\frac{0.001}{20}$
• C. $\frac{10}{0.2}$
• D. $10\%$

Hint:

Always simplify fractions and percentages first.
Any value greater than $1$ (or $100\%$) or less than $0$ can never represent a probability.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks us to identify which of the given values cannot represent the probability of an event.
Probability is a measure of the likelihood of an event occurring.

Step 2: Key Formula or Approach:
For any event $E$, the probability $P(E)$ must lie within the closed interval $[0, 1]$:
\[ 0 \le P(E) \le 1 \]
A probability cannot be less than $0$ (negative) and cannot be greater than $1$.
We will convert each option to its standard decimal form and check if it lies in this valid range.

Step 3: Detailed Explanation:

• Let us analyze the value of each option:
- Option (A): $\frac{39}{100}$
\[ \frac{39}{100} = 0.39 \]
Since $0 \le 0.39 \le 1$, this is a valid probability.
- Option (B): $\frac{0.001}{20}$
\[ \frac{0.001}{20} = \frac{1}{20000} = 0.00005 \]
Since $0 \le 0.00005 \le 1$, this is a valid probability.
- Option (C): $\frac{10}{0.2}$
\[ \frac{10}{0.2} = \frac{10 \times 10}{2} = \frac{100}{2} = 50 \]
Since $50 \gt 1$, this value lies outside the maximum possible limit of a probability. Therefore, it cannot be the probability of any event.
- Option (D): $10\%$
\[ 10\% = \frac{10}{100} = 0.1 \]
Since $0 \le 0.1 \le 1$, this is a valid probability.


Step 4: Final Answer:
Hence, $\frac{10}{0.2}$ cannot be the probability of an event.