Getting a natural number greater than zero is an example of a sure event within the field of probability.
Understanding the Concept of a Sure Event
A sure event, also known as a certain event, is an outcome or set of outcomes in a probability experiment that is guaranteed to happen. Its probability is always 1 (or 100%). This concept is fundamental to understanding the likelihood of various occurrences.
Why 'Getting a Natural Number Greater Than Zero' is a Sure Event
The key to understanding why this is a sure event lies in the definition of natural numbers. In mathematics, natural numbers (often denoted by $\mathbb{N}$) typically start from 1 and go upwards indefinitely (1, 2, 3, 4, ...). While some definitions include 0, the most common and standard definition for "natural numbers" in this context refers to positive integers.
Since every natural number (1, 2, 3, ...) is inherently greater than zero, selecting any natural number will always result in a number greater than zero. There is no possibility of selecting a natural number that is not greater than zero.
As explicitly stated by a reference: "Getting a natural number greater than zero is an example of a sure event because it is certain to occur. So, the correct option is (b) Sure event." Source: Brainly.in
Types of Events in Probability
To further contextualize sure events, it's helpful to compare them with other common types of events in probability:
| Event Type | Definition | Probability Range | Example |
|---|---|---|---|
| Sure Event | An event that is certain to occur. | 1 (or 100%) | Selecting a natural number from a set of natural numbers (it will always be greater than zero). |
| Impossible Event | An event that cannot occur under any circumstances. | 0 (or 0%) | Rolling an 8 on a standard six-sided die. |
| Random Event | An event that has a chance of occurring, but is not certain. | > 0 and < 1 | Flipping a coin and getting heads. |
Practical Insights
- Definition Matters: The classification of an event often depends on the precise definition of the terms involved. For "natural numbers," the common understanding (positive integers) makes this a sure event. If "natural numbers" included negative numbers or zero was not the boundary, the classification might change.
- Probability Scale: Events are measured on a probability scale from 0 (impossible) to 1 (sure). Understanding where an event falls on this scale helps in predicting outcomes and making informed decisions.
