A spinner is divided into eight equal-sized sections, numbered from 1 to 8, inclusive.

What is true about spinning the spinner one time? Check all that apply.

~ S = {1, 2, 3, 4, 5, 6, 7, 8}

~If A is a subset of S, A could be {1, 2, 3}.

~If A is a subset of S, A could be {7, 8, 9}.

~If a subset A represents spinning a number less than 4, its sample space is A = {1, 2, 3, 4}.

~ If a subset A represents the complement of spinning an odd number, its sample space is A = {2, 4, 6, 8}.

{ 9 } ∉ S. Answer C is not correct.
If subset A represent spinning a number less than 4, its sample space is
A ={ 1, 2 , 3 }. Therefore D is also false.
Answer:
True statements are;
A ) S = { 1, 2, 3, 4, 5, 6, 7, 8 }.
B ) If A is a subset if S, A could be { 1, 2, 3 }.
E ) If a subset A represents the complement of spinning an odd number, its sample space is A = { 2, 4, 6, 8 }.

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astha8579 astha8579 · Answer 2 · 2022-02-15T07:55:45-05:00

The true options about spinning the spinner one time are:

Option 1: S = {1, 2, 3, 4, 5, 6, 7, 8}
Option 2: If A is a subset of S, A could be {1, 2, 3}
Option 5: If a subset A represents the complement of spinning an odd number, its sample space is A = {2, 4, 6, 8}

What is a sample space for a random experiment?

An experimenter do some random experiments which has some fixed set of outputs. That set of all possible outputs of that experiment is called sample space.

What is a subset of a given set?

Subset of a given set is a set whose all elements are in the original set of which it is subset.

So if B is subset of A, then all elements of B are in A but it is not necessary that all elements of A are in B.

If B is subset of A, then A is superset of B.

What is complement of a set?

Complement of a set exist if there is a superset in consideration. Usually it is the universal set (the biggest superset for the given context)

Suppose that U is the universal set and A is its subset.

Then A' is called complement of A and contains those elements of U which are not in A. (so that both A and A' completely contain all element of U and no repetition in each other)

Using the above definitions, we can say that:

For the given case, as there are 8 parts from 1 to 8 in the spinner and spinner when gets spin, stops at certain number. That number will be from 1 to 8 only. So the sample space we get is {1,2,3,4,5,6,7,8}
Thus, S = {1,2,3,4,5,6,7,8} (usually we denote sample space by symbol S).

Subset of S can be {1,2,3} but cannot be {7,8,9} as 9 doesn't belong to S

If a subset A represents spinning a number less than 4, its sample space is A = {1, 2, 3, 4}. (its incorrect as 4 itself is not less than 4. For this experiment, the sample space would contain 3 items which are 1, 2, and 3.

If a subset A represents the complement of spinning an odd number, its sample space is A = {2, 4, 6, 8}. It is correct since if we focus only on non-odd numbers, the rest of the numbers are going to be even as in integers, a number is either even or odd.

Thus,

The true options about spinning the spinner one time are:

Option 1: S = {1, 2, 3, 4, 5, 6, 7, 8}
Option 2: If A is a subset of S, A could be {1, 2, 3}
Option 5: If a subset A represents the complement of spinning an odd number, its sample space is A = {2, 4, 6, 8}

Learn more about sample space here:

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