A production facility employs 20 workers on the day shift, 15 workers on the swi

Question

A production facility employs 20 workers on the day shift, 15 workers on the swing shift, and 10 workers on the graveyard shift. A quality control consultant is to select 7 of these workers for in-depth interviews. Suppose the selection is made in such a way that any particular group of 7 workers has the same chance of being selected as does any other group (drawing 7 slips without replacement from among 45). (Enter your answers to four decimal places.)

(a) How many selections result in all 7 workers coming from the day shift?
1

What is the probability that all 7 selected workers will be from the day shift?
2

(b) What is the probability that all 7 selected workers will be from the same shift?
3

(c) What is the probability that at least two different shifts will be represented among the selected workers?
4

(d) What is the probability that at least one of the shifts will be unrepresented in that sample of workers?
5

Explanation / Answer

a. for this question I assume that it is meant to say that you can select as many as times you want. because only then 'how many selections' this phrase makes sense.

If first 25 times we select from other shifts exceft day shift then also after this all the selections will have to be done from day shift. so 25+7 =32 selections will result is all day shitft

this probability is 20c7/45c7 =1.7*10-3

b. What is the probability that all 7 selected workers will be from the same shift

it will be ( 20c7 + 15c7 + 10c7 ) / 45c7 = 1.85*10-3

c. 1- probability calculated in b = 0.998

d. (35c7 + 30c7 +25c7 ) / 45c7 =0.2036

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