Question

What is the probability of an impossible event?

• A. \(1\)
• B. \(0.5\)
• C. \(0\)
• D. \(-1\)

Hint:

Remember the three fundamental probability cases:
• Impossible event → \(P = 0\)
• Certain event → \(P = 1\)
• All other events → \(0<P<1\)

Answer 1

The Correct Option is C

Concept: Probability measures the likelihood of an event occurring. Its value always lies between \(0\) and \(1\). \[ 0 \le P(E) \le 1 \] where \(P(E)\) represents the probability of an event \(E\). The important cases are:
• \(P(E) = 1\) → certain event
• \(0<P(E)<1\) → possible event
• \(P(E) = 0\) → impossible event

Step 1: Understand an impossible event. An impossible event is an event that cannot occur under any circumstance. For example:
• Getting a number \(7\) when rolling a standard die.
• Getting a head when the coin shows only tails.

Step 2: Apply the probability definition. Since the event cannot occur, the number of favourable outcomes is zero. Using the probability formula: \[ P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}} \] \[ P(E) = \frac{0}{n} = 0 \]

Step 3: Final result. Thus, the probability of an impossible event is \[ \boxed{0} \]