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:
We need to determine which of the given values cannot represent the probability of an event.

Step 2: Key Formula or Approach:
The probability of any event $E$, denoted as $P(E)$, must always satisfy the following inequality:
\[ 0 \le P(E) \le 1 \]
A probability cannot be negative, and it cannot be greater than $1$. We will evaluate each option in its decimal format.

Step 3: Detailed Explanation:

• Evaluate Option (A):
\[ \frac{39}{100} = 0.39 \]
Since $0 \le 0.39 \le 1$, this can be a valid probability.

• Evaluate Option (B):
\[ \frac{0.001}{20} = 0.00005 \]
Since $0 \le 0.00005 \le 1$, this can be a valid probability.

• Evaluate Option (C):
\[ \frac{10}{0.2} = \frac{100}{2} = 50 \]
Since $50 \gt 1$, this value exceeds the maximum limit for a probability. Therefore, it cannot be a probability of any event.

• Evaluate Option (D):
\[ 10\% = \frac{10}{100} = 0.1 \]
Since $0 \le 0.1 \le 1$, this can be a valid probability.


Step 4: Final Answer:
The value that cannot represent the probability of an event is $\frac{10}{0.2}$.