Briefly describe an impossible event and a sure event. What is the probability of the occurrence of each of these two events?
The correct answer and explanation is :
An impossible event is an event that can never occur under any circumstances. An example of an impossible event is rolling a standard six-sided die and getting a result of 7. Since the die only has faces numbered 1 through 6, rolling a 7 is not possible. The probability of an impossible event occurring is 0.
A sure event (also called a certain event) is an event that is guaranteed to happen. An example of a sure event is the sun rising tomorrow. Barring extraordinary cosmic events, the sun will always rise, making this event certain. The probability of a sure event occurring is 1.
Explanation:
Probability is a measure of how likely an event is to happen. It is expressed as a number between 0 and 1, where:
- 0 means the event will never happen (impossible event).
- 1 means the event will always happen (sure event).
- Values between 0 and 1 indicate the event has a chance of occurring but is not guaranteed.
For an impossible event, the number of favorable outcomes is zero, meaning the probability is:
[
P(\text{impossible event}) = \frac{0}{\text{total possible outcomes}} = 0
]
For a sure event, all possible outcomes favor the event occurring, meaning the probability is:
[
P(\text{sure event}) = \frac{\text{total possible outcomes}}{\text{total possible outcomes}} = 1
]
Understanding these concepts helps in probability theory, where events are classified based on their likelihood. In real-world applications, nearly impossible events (like winning the lottery) have probabilities close to zero, while nearly sure events (like water freezing at 0°C under normal pressure) have probabilities close to one.