Questions: 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? (Type an integer or a decimal.)

Solution Steps

To solve the given problem, we need to understand the concept of probability. The probability of an impossible event is always zero. This is a fundamental principle in probability theory. Additionally, if a probability is approximated to be zero based on empirical results, it does not necessarily mean that the event is impossible; it just means that it is very unlikely to occur.

1. The probability of an impossible event is zero.
2. An empirical probability close to zero indicates a very low likelihood, not impossibility.

In probability theory, the probability of an event that cannot occur is defined as \( P(A) = 0 \). This means that if an event is impossible, it has no chance of happening.

When we approximate a probability based on empirical results, we may find that it is very close to zero. However, this does not imply that the event is impossible; it simply indicates that the event is highly unlikely to occur. Thus, \( P(A) \approx 0 \) does not mean \( P(A) = 0 \).

Final Answer