Question

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

• A. 4/3
• B. 2/3
• C. 1
• D. 3/5

Hint:

To quickly identify if a fraction can be a probability, check if it's a proper fraction (numerator is smaller than the denominator). If it is, its value is between 0 and 1. If it's an improper fraction (numerator is greater than or equal to the denominator), its value is greater than or equal to 1. Only improper fractions equal to 1/1, 2/2 etc., are valid probabilities.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
The probability of any event is a number that represents the likelihood of that event occurring. This number must always fall within a specific range.
Step 2: Key Formula or Approach:
The fundamental rule of probability states that for any event E, its probability P(E) must satisfy the condition:
\[ 0 \le P(E) \le 1 \] This means probability can be 0 (for an impossible event), 1 (for a certain event), or any value in between. It can never be negative or greater than 1.
Step 3: Detailed Explanation:
Let's evaluate each option to see if it falls within the range [0, 1].
(A) \( \frac{4}{3} \): This is an improper fraction. \( \frac{4}{3} = 1.333... \). Since this value is greater than 1, it cannot be the probability of any event.
(B) \( \frac{2}{3} \): This value is approximately 0.667. It is between 0 and 1, so it can be a probability.
(C) 1: This is a valid probability, representing a certain event.
(D) \( \frac{3}{5} \): This value is 0.6. It is between 0 and 1, so it can be a probability.
Based on the analysis, \( \frac{4}{3} \) is the only value that cannot represent a probability.
Step 4: Final Answer:
The value \( \frac{4}{3} \) cannot be the probability of any event.