If an event cannot occur, then its propbability is

Options

A. 1
B. `(3)/(4)`
C. `(1)/(2)`
D. 0

Explanation

To find the probability of an event that cannot occur, we can follow these steps:

### Step 1: Understand the Concept of an Event
An event in probability is a specific outcome or a set of outcomes from a random experiment.

**Hint:** An event can be anything from rolling a die to drawing a card from a deck.

### Step 2: Define an Impossible Event
An impossible event is one that cannot happen. For example, rolling a 7 on a standard six-sided die is impossible.

**Hint:** Think about scenarios where there are no possible outcomes that satisfy the event.

### Step 3: Determine the Favorable Outcomes
For an impossible event, the number of favorable outcomes is 0 because there are no outcomes that can occur.

**Hint:** Recall that favorable outcomes are the outcomes that would make the event true.

### Step 4: Identify the Sample Space
The sample space is the set of all possible outcomes of an experiment. For a six-sided die, the sample space is {1, 2, 3, 4, 5, 6}.

**Hint:** The sample space always contains at least one outcome, but the impossible event has none.

### Step 5: Calculate the Probability
The probability of an event is calculated using the formula:
\[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Number of Outcomes in Sample Space}} \]
For an impossible event:
\[ \text{Probability} = \frac{0}{n} = 0 \]
where \( n \) is the total number of outcomes in the sample space.

**Hint:** Remember that dividing zero by any non-zero number results in zero.

### Conclusion
Thus, the probability of an event that cannot occur (an impossible event) is always 0.

**Final Answer:** The probability of an event that cannot occur is 0.