Define each of the following.


f. Impossible event

Verified step by step guidance

1. Understand that in probability theory, an event is a set of outcomes from a random experiment.
2. An impossible event is an event that cannot occur under any circumstances in the given experiment.
3. Formally, the probability of an impossible event is zero, which can be written as \(P(\text{impossible event}) = 0\).
4. For example, if you roll a standard six-sided die, the event of rolling a 7 is impossible because 7 is not a possible outcome.
5. Thus, defining an impossible event involves recognizing that it has no outcomes in the sample space and its probability is zero.

Key Concepts

Impossible Event

An impossible event is an outcome in a probability experiment that cannot occur under any circumstances. Its probability is always zero, meaning there is no chance of it happening. For example, rolling a 7 on a standard six-sided die is an impossible event.

Probability of an Event

The probability of an event measures the likelihood that the event will occur, expressed as a number between 0 and 1. A probability of 0 means the event is impossible, while a probability of 1 means the event is certain. Understanding this helps in classifying events like impossible or certain.

Sample Space

The sample space is the set of all possible outcomes in a probability experiment. It provides the context for defining events, including impossible events, which are subsets of the sample space with no elements. Knowing the sample space is essential to identify and define events properly.