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Consider an experiment of choosing randomly two of the letters from the alphabet.
(a) Find the sample space S1 of the experiment if it possible to choose the same letter twice.
(b) Find the sample space S2 of the experiment if it is not possible to choose the same letter twice.
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As the "experiment" is described in the post, this description is not complete.
To be complete, the problem must say what is recorded as the experiments' result.
If you record the letters as the pairs (X,Y), where the order does matter, it is one experiment.
If you record the letters as the pairs (X,Y) and the order does not matter, it is another experiment.
In this another experiment, the pair is (X,Y) considered the same as (Y,X),
while in the first experiment these pairs are different.
As you will see from what follows, the sample spaces are DIFFERENT in these experiments.
Unfortunately, the problem / (the post) is silent about it, so I will make my own assumptions.
* * * Let's consider first the case, when the order does matter. * * *
(a) Find the sample space S1 of the experiment if it possible to choose the same letter twice
Then the sample space S1 is the space of all the pairs (X,Y), where X and Y are letters
from the alphabet and the order does matter.
You may think about this sample space S1 as about the (26x26)-matrix of the pairs of the letters.
The size (the number of elements) of the sample space is 26*26 = = 676 in this case.
(b) Find the sample space S2 of the experiment if it is not possible to choose the same letter twice
Then the sample space S2 is the space of all the pairs (X,Y), where X and Y are DIFFERENT letters
from the alphabet and the order does matter. The pairs of the form (X,X) are not allowed.
You may think about this sample space S2 as about the (26x26)-matrix of the pairs of the letters WITH EXCLUDED DIAGONAL.
The size (the number of elements of the sample space is 26*26 - 26 = = 676 - 26 = 650 in this case.
At this point, the consideration of the first case is FULLY COMPLETED.
* * * Next, let's consider the case, when the order in pairs does not matter. * * *
(a) Find the sample space S1 of the experiment if it possible to choose the same letter twice
Then the sample space S1 is the space of all the pairs (X,Y), where X and Y are letters
from the alphabet and the order DOES NOT matter: the pair (X,Y) is the same as (Y,X).
You may think about this sample space S1 as about the UPPER the DIAGONAL part of the (26x26)-matrix
of the pairs of the letters; the diagonal of the matrix is included to the sample space S1.
The size (the number of elements) of the sample space S1 is = 13*27 = 351 in this case.
(b) Find the sample space S2 of the experiment if it is not possible to choose the same letter twice
Then the sample space S2 is the space of all the pairs (X,Y), where X and Y are DIFFERENT letters
from the alphabet and the order DOES NOT matter. The pairs of the form (X,X) are not allowed.
You may think about this sample space S2 as about the UPPER the DIAGONAL part of the (26x26)-matrix of the pairs of the letters
WITH EXCLUDED DIAGONAL of the matrix.
The size (the number of elements) of the sample space S2 is = 13*27-26 = 351 - 26 = 325 in this case.
At this point, the solution of the problem is FULLY COMPLETED.