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pwoz
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The question is as follows:
Suppose a lot of 50 electrical components contains five components that are defective. The lot is randomly divided among five customers, with each customer receiving 10 components.
Calculate the probabilities of the following events:
a. Each customer receives one defective component.
b. One customer receives all five defective components.
c. Two customers receive two defective components, one receives one, and the other two receive no defective components.
I'm looking for help as to why N(S) and N(X) are constructed the way they are.
I constructed N(S) as follows
[PLAIN]http://img203.imageshack.us/img203/2478/20647565.jpg
My understanding is the 5! in the denominator is because the order that the widgets are assigned does not matter. ie, the "first" person going first is the same as the "second" person going first.
To this end I constructed the formula for part A as:
[PLAIN]http://img27.imageshack.us/img27/4980/87152546.jpg
My logic on the coefficient is the same as before. It does not matter who goes first.
Part b was constructed as:
[PLAIN]http://img683.imageshack.us/img683/8265/11889894.jpg
I set the coefficient this way since there are 5 ways to pick the person who gets all of the defective widgets, and it doesn't matter who.
Part c:
[PLAIN]http://img265.imageshack.us/img265/7426/51203459.jpg
Again, I set the coefficient up as 5 ways to pick the first person, 4 for the second, and 3 for the last person to receive one.
I'm fairly certain I am not thinking about the coefficient term correctly. I'm not looking for a solution to these problems, rather I'm trying to understand the setup. Something about this topic has never clicked with me. Any guidance is appreciated.
Suppose a lot of 50 electrical components contains five components that are defective. The lot is randomly divided among five customers, with each customer receiving 10 components.
Calculate the probabilities of the following events:
a. Each customer receives one defective component.
b. One customer receives all five defective components.
c. Two customers receive two defective components, one receives one, and the other two receive no defective components.
I'm looking for help as to why N(S) and N(X) are constructed the way they are.
I constructed N(S) as follows
[PLAIN]http://img203.imageshack.us/img203/2478/20647565.jpg
My understanding is the 5! in the denominator is because the order that the widgets are assigned does not matter. ie, the "first" person going first is the same as the "second" person going first.
To this end I constructed the formula for part A as:
[PLAIN]http://img27.imageshack.us/img27/4980/87152546.jpg
My logic on the coefficient is the same as before. It does not matter who goes first.
Part b was constructed as:
[PLAIN]http://img683.imageshack.us/img683/8265/11889894.jpg
I set the coefficient this way since there are 5 ways to pick the person who gets all of the defective widgets, and it doesn't matter who.
Part c:
[PLAIN]http://img265.imageshack.us/img265/7426/51203459.jpg
Again, I set the coefficient up as 5 ways to pick the first person, 4 for the second, and 3 for the last person to receive one.
I'm fairly certain I am not thinking about the coefficient term correctly. I'm not looking for a solution to these problems, rather I'm trying to understand the setup. Something about this topic has never clicked with me. Any guidance is appreciated.
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