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A corporation is sampling without replacement for n = 3
Chapter 3, Problem 110E(choose chapter or problem)
Problem 110E
A corporation is sampling without replacement for n = 3 firms to determine the one from which to purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are local and two are not local. Let Y denote the number of nonlocal firms among the three selected.
a P ( Y = 1).
b P ( Y ≥ 1).
c P ( Y ≤ 1).
Questions & Answers
QUESTION:
Problem 110E
A corporation is sampling without replacement for n = 3 firms to determine the one from which to purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are local and two are not local. Let Y denote the number of nonlocal firms among the three selected.
a P ( Y = 1).
b P ( Y ≥ 1).
c P ( Y ≤ 1).
ANSWER:
Solution :
Step 1 of 3:
Let N denote the sample is to be selected from a pool of six firms.
In the 6 firms 4 are local and 2 are not local.
The Y= the number of nonlocal firms among the 3 selected.
Our goal is:
a). We need to find P(Y=1).
b). We need to find P(Y1).
c). We need to find P(Y1).
a).
Given P(Y=1).
Now we have to find P(Y=1).
The formula of the hypergeometric probability is
p(y)=
Where N=population size.
n= Number of draws.
r= Number of observed success.
We know that N=6, n=3 and r=2.
Then we substitute all the values.
p(1)=
p(1)=
p(1)=
p(1)=
p(1)= 0.6
Therefore, P(Y=1) is 0.6.