https://file.aiquickdraw.com/mathbot/file/17255310402427q3xs3nj.jpg

The image appears to contain a probability-related problem. Let me extract and solve it for you.

The text seems to describe a scenario with two probabilities:
- A machine operates successfully with a probability of \(0.92\).
- If it fails, it will fail again with a probability of \(0.65\).

Two questions are asked:
1. What is the probability of a failure?
2. Given that it has occurred, what is the probability that a failure is recorded on the second run?

Let me calculate the answers for these questions:

1. The probability of a failure (P(failure)) is simply the complement of the success probability:
   \[
   P(failure) = 1 - P(success) = 1 - 0.92
   \]

2. Given that a failure has occurred on the first run, the probability of failure on the second run is given as \(0.65\). Thus, the second part involves conditional probability.

I'll calculate these now.1. The probability of a failure is \( P(failure) = 0.08 \) or 8%.
   
2. Given that a failure has occurred, the probability that a failure is recorded on the second run is \( 0.65 \) or 65%.

Would you like further details or explanations on these concepts?

Here are five related questions to expand your understanding:
1. How do you calculate the probability of multiple independent events?
2. What is conditional probability and how does it apply to dependent events?
3. How would the result change if the machine had a different success rate?
4. How do you calculate the probability of at least one failure in two trials?
5. Can you calculate the expected number of failures over several trials?

**Tip:** Understanding the complement rule is key to solving many probability problems. It states that the probability of an event not occurring is 1 minus the probability that it does occur.

A machine operates with a success rate (P(success)) of 0.92. If a failure occurs, the probability of failing again is 0.65. What is the probability of failure on the first attempt? Given that a failure has occurred, what is the probability of a failure on the second attempt?

This problem involves calculating the probability of a machine failing given a success rate of 0.92. Additionally, it explores conditional probability where the machine, once failed, has a 0.65 chance of failing again. Understand core concepts like the complement rule and conditional probability through this step-by-step solution.

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