# Probability: Is the manager telling the truth?

• sanctifier
In summary, the conversation discusses the accuracy of a manager's claim that 99% of the products produced in their factory are flawless. It is suggested that further testing is needed to determine if the manager is telling the truth, as a probability of 7.5% is still reasonable and does not definitively prove that the manager lied.
sanctifier

## Homework Statement

The manager of a factory proclaims 99% of the products manufactured in his factory are unflawed. If we draw 50 products from 5000 products and find 2 of 50 are flawed, then how do we know the manage is telling the truth?

Nothing special.

## The Attempt at a Solution

$\frac{{5000*0.99 \choose 48} {5000*0.01 \choose 2}}{ {5000 \choose 50}} \approx 0.0754$

Manager lied.

Is this correct? Thank you in advance!

You cannot conclude that the manager lied based on this result. You could have been unlucky with the 50 products. A probability of 7.5% is still reasonable and needs more tests before such a strong conclusion can be drawn.

## 1. What is probability and how is it related to the manager's truthfulness?

Probability is the likelihood or chance of an event occurring. In this case, it is the likelihood of the manager telling the truth. Probability is related to the manager's truthfulness because it can help us determine the likelihood of their statement being true or false.

## 2. What factors affect the probability of the manager telling the truth?

There are many factors that can affect the probability of the manager telling the truth, such as their past behavior, their motives, the evidence supporting their statement, and the credibility of the source of the information.

## 3. How can we calculate the probability of the manager telling the truth?

There is no definitive way to calculate the probability of the manager telling the truth, as it is subjective and can vary depending on the situation. However, we can use statistical methods and analyze the available data to make an informed estimate of the probability.

## 4. Can we ever be 100% certain about the manager's truthfulness based on probability?

No, probability can only give us an estimate of the likelihood of the manager telling the truth. It cannot provide us with absolute certainty, as there is always a chance that the manager may be lying or telling the truth by coincidence.

## 5. How can we use probability to make decisions about the manager's statement?

We can use probability to assess the reliability of the manager's statement and weigh it against other factors, such as evidence and credibility. This can help us make a more informed decision about whether to believe the manager's statement or not.

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