Question

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

• A. 0
• B. \(\frac{4}{5}\)
• C. \(\frac{5}{4}\)
• D. 1

Answer 1

The Correct Option is C

The probability of an event must satisfy the condition that it is a number between 0 and 1, inclusive. This means:

• 0: Represents an impossible event.
• 1: Represents a certain event.
• \(\frac{4}{5}\): This is a fraction that lies between 0 and 1, representing a valid probability.

Examine the option:

• \(\frac{5}{4}\): This equals 1.25, which is greater than 1. As probabilities cannot exceed 1, \(\frac{5}{4}\) cannot represent a probability.

Thus, the value \(\frac{5}{4}\) cannot be the probability of any event, as it does not satisfy the probability range.

Answer 2

Given: The probability of an event must lie between \( 0 \) and \( 1 \), inclusive.

Step 1: Understanding Probability Range 

- Probability of any event \( P(E) \) satisfies: \[ 0 \leq P(E) \leq 1 \]

Step 2: Checking the Given Options

- \( 0 \) is a valid probability (impossible event). - \( \frac{4}{5} = 0.8 \), which is within the valid range. - \( \frac{5}{4} = 1.25 \), which is greater than \( 1 \), so it is not a valid probability. - \( 1 \) is a valid probability (certain event).

Final Answer: \(\frac{5}{4}\)