Answer :
Answer:
All possible are:
(G,L,S)
(G,L,R)
(G,L,P)
(G,S,R)
(G,S,P)
(G,R,P)
(L,S,R)
(L,S,P)
(S,R,P)
{L,R,P)
Probability of 1st/2nd/10th sample = 1/10
Step-by-step explanation:
All the possible combinations of the 3 size samples from a 5 size population have been listed without repetition.
Total Numbers of Samples = 10
To find the probability of finding the first sample from random sampling procedure,
Probability = Number of desired outcomes/ Total number of outcomes
Where Number of desired outcome is 1 and total number of outcomes is 10.
Probability = 1/10
Similarly, to find 2nd sample or 10th sample, the number of desired outcomes is same i.e 1, hecne the probability remains the same i.e 1/10
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
a) Given:
Population size [tex]N=5[/tex].
Sample size [tex]n=2[/tex]
Possible sample (without replacement)
[tex]\Rightarrow 5C_{2}=\frac{5!}{2!\times 3!}[/tex]
[tex]=\frac{5\times 4}{2}[/tex]
[tex]=10[/tex]
[tex]10 samples:-[/tex]
Governor, Lieutenant Governor, secretary of state, Attorney General, Press (P)
Possible samples:
(G,L), (G,S), (G,A), (G,P), (L,S), (S,A), (A,P), (L,P), (S,P), (A,L).
b) Event: [tex]E\to[/tex]choosing sample second and tenth.
[tex]E=\left\{\left ( G,S \right ),\left ( A,L \right ) \right\}\\n\left ( E \right )=2\\n(S) =10[/tex]
The Probability of that it is the first sample.
Second and tenth sample[tex]=\frac{n\left ( E \right )}{n(S)}[/tex]
[tex]=\frac{2}{10}[/tex]
[tex]=\frac{1}{5}[/tex]
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