Question

In designing an experiment involving a treatment applied to 4 test​ subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects.​ (Recall that with a simple random​ sample, all samples of the same size have the same chance of being​ selected.) Answer the question below.
What is the probability of each simple random sample in this​case?

Answer 1

Answer:

The probability is  $p(n ) = 3.18*10^{-5}$

Step-by-step explanation:

From the question we are told that

     The population size is  N =  31

      The sample size  n =  4  

 

Generally the number of way by which the n  can be selected from N is mathematically represented as

          $\left N} \atop {}} \right. C_n = \frac{N! }{(N-n)!n!}$

=>       $\left 31} \atop {}} \right. C_4 = \frac{31! }{(31-4)!4!}$

=>       $\left 31} \atop {}} \right. C_4 = \frac{31 * 30 * 29 * 28* 27! }{27! * 4*3 * 2 * 1 }$

=>        $\left 31} \atop {}} \right. C_4 = \frac{ 755160 }{ 24}$

=>        $\left 31} \atop {}} \right. C_4 = 31465$

The number of ways of selecting a particular sample size is  is   $k = 1$

Therefore the probability of each simple random sample in this​ case is mathematically evaluated as  

           $p(n ) = \frac{1}{31465}$  

           $p(n ) = 3.18*10^{-5}$