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?

## Answers and Replies

Homework Helper
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.