Question:
Which of the following cannot be the probability of an event?
Which of the following cannot be the probability of an event?
Updated On: Apr 28, 2025
- 0
- \(\frac{4}{5}\)
- \(\frac{5}{4}\)
- 1
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The Correct Option is C
Approach Solution - 1
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.
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Approach Solution -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: \(\frac{5}{4}\)
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