• MechatronO
In summary, the speaker is seeking clarification on an exercise in their probability and statistics course. The exercise involves calculating the probability of producing an unacceptable lot, with the given information that the probability of a lot being unacceptable is 0.05. The speaker is unsure about the wording in part (e) of the exercise and suggests a different formulation. However, the expert believes that the original formulation is correct and explains the reasoning behind it.

#### MechatronO

I'm taking a course in probability and statistics and encountered an exercise with a formulation that doesn't make sense at all to my English-as-second-language ears.

I will recite the exercise here and maybe you could help my settle wether if the original formulation is bad, or if I've found an opportunity to learn a new way of formulating myself in English.

The exercise is from "Introduction to Probability and Statistics" by J.Susan Milton and Jesse C. Arnold (McGraw-Hill 2004).

I'll quote some excerpts that I think will provide enough information.

Section 3.4, ex. 25:

...Assume that the probability that a given a lot is unacceptable is .05. Let X denote the number of runs conducted to produce an unacceptable lot. Assume that the runs are independent in the sense that the outcome of one run has no effect on that of any other.
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(e) Find the probability that the number of runs required to produce an unacceptable lot is at least 3.

The density function is given by

f(x) = (1-p)x-1*p (geometric)

where p=.05

Now (e) doesn't make any sense at all to me. What makes least sense is the use of "that".

It's solved by

P(X≥3) = 1-( f(1) + f(2) )

However, a more appropriate formulation of (e) I then think would be for instance:

Calculate the probability of finding an unacceptable lot when the number of runs are at least 3.

What do you think? Is the original formulation of (e) good, quite inprecise or even incorrect?

It means, 2 runs produce no unacceptable lots. Therefore you need at least 3 to produce an unacceptable lot. So you want the probability p that the first 2 runs are acceptable.

It is phrased correctly.

## 1. What is the purpose of this formulation?

The purpose of a formulation is to create a specific mixture of ingredients or chemicals in order to achieve a desired outcome. This could be anything from a medication to a cleaning product.

## 2. How is this formulation different from others on the market?

The difference between formulations lies in the specific ingredients and their concentrations. Each formulation is unique and designed to serve a specific purpose or address a specific problem.

## 3. Are there any potential side effects or risks associated with this formulation?

It is important to thoroughly test and evaluate a formulation before it is released to the market. This includes assessing any potential risks or side effects. However, it is always important to follow usage instructions and consult a professional if you have any concerns.

## 4. How do you determine the effectiveness of this formulation?

The effectiveness of a formulation is typically determined through rigorous testing and experimentation. This can involve conducting trials, analyzing data, and comparing the results to existing formulations or standards.

## 5. Can this formulation be modified for different purposes?

Depending on the ingredients and their properties, a formulation can often be modified or adapted for different purposes. However, thorough testing and evaluation must be conducted to ensure safety and effectiveness for the new purpose.