Question 1196655: A sequence of two different digits is randomly chosen from the digits 0-4; the first digit is larger than the second.
Describe the sample space S of the experiment. (Select all that apply.)
40 41 42 43
01 02 04 05
01 02 03 04
30 31 32 34
20 21 23 24
42 43 44 45
11 22 33 44
21 22 23 25
10 12 13 14
List the elements of the given event. (Select all that apply.)
10
30 31 32
20 21
23 24
30 32 34 43
21
12
40 41 42 43
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3817)   (Show Source):
You can put this solution on YOUR website!
If the first digit is 1, then the second digit must be 0 since "The first digit is larger than the second" is given to us.
Therefore, this forms the number 10 as the only possibility for this case.
If the first digit is 2, then we could have either 20 or 21
If the first digit is 3, then we could have either 30, 31, or 32
If the first digit is 4, then we could have either 40, 41, 42, or 43
Here's the entire sample space
{
10
20,21
30,31,32
40,41,42,43
}
Each row has a different tens digit to help break things up better.
Though if you wanted you can list everything on one single line like this
{10,20,21,30,31,32,40,41,42,43}
We can see that 10 is a potential answer choice, and so is something like 30 31 32
However something like 12 is NOT a potential answer.
Also, anything involving 5 isn't an answer since it's not in the range from 0 to 4.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The wording of the problem is invalid; or, at best, extremely awkward.
1st question....
"A sequence of two different digits is randomly chosen from the digits 0-4; the first digit is larger than the second."
"Describe the sample space S of the experiment."
The sample space is DESCRIBED in the statement of the problem -- it is all ordered pairs of digits AB in which A and B are chosen from the digits 0 to 4, and A is greater than B.
So the instruction to "describe" the sample space does not ask the student to do anything.
Presumably the intended question was to define precisely the sample space of the experiment. That sample space contains 10 elements; you can't define the sample space of 10 elements exactly by looking at sets of 4 2-digit strings and "selecting all that apply".
2nd question....
"List the elements of the given event. (Select all that apply.)"
It is nonsensical to "list" the elements of the given event by selecting, from among lists of 2-digit numbers, ones that satisfy the conditions of the event.
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