Question
\( 10(5.1,5.2) \) What is the probability of an event that is impossible? Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible? What is the probability of an event that is impossible? 0 (Type an integer or a decimal.) Suppose that a probability is approximated to be zero based on empirical results. Does this mean that the event is impossible? \( 26 \% \), 13 of 50 points No 1 Port Yes
Ask by Ball Dickson. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability of an impossible event is 0. A probability approximated to be zero does not mean the event is impossible; it just means it's very unlikely to occur.
Solution
To address your questions, let's break them down step by step.
1. **What is the probability of an event that is impossible?**
- The probability of an impossible event is defined as \(0\). This means that if an event cannot occur under any circumstances, its probability is \(0\).
2. **Does a probability approximated to be zero based on empirical results mean that the event is impossible?**
- Not necessarily. A probability that is approximated to be zero based on empirical results indicates that the event is highly unlikely to occur, but it does not mean that it is impossible. There may still be a very small chance that the event could occur, even if it is not observed in the data.
### Summary:
- The probability of an impossible event is \(0\).
- A probability approximated to be zero does not imply that the event is impossible; it may just be very unlikely.
### Answers:
- Probability of an impossible event: **0**
- Does a probability approximated to be zero mean the event is impossible? **No**
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
An impossible event has a probability of exactly 0. In the world of probabilities, this means that under no circumstances can the event occur. For instance, rolling a 7 on a standard six-sided die is impossible, so it gets a firm score of zero on the probability scale! Now, just because empirical evidence suggests a probability is very close to zero does not automatically denote impossibility. It’s entirely possible for an event to have a very low probability based on observed data, yet still have a non-zero chance of occurring. Think of rare events, like winning the lottery—extremely unlikely, but definitely not impossible!
