Remember state space refers to the space of all potential possibilities. Which dichotomous questions below will successfully narrow down the entire state space of "flipping a coin and rolling a normal six-sided die" to just 1 outcome?
1. Did the coin land on heads?
2. Is the value on the die odd?
3. Is the value on the die more than 3?
4. Does the value on die equal 1, 2, 5, or 6?

The correct answers to the question are

1. Did the coin land on heads?

2. Is the value on the die odd?

3. Is the value on the die more than 3?

4. Does the value on die equal 1, 2, 5, or 6?

Step-by-step explanation:

A dichotomous question is one that has only two possible responses or answers such as Yes or No, Agree or Disagree. Dichotomous question are used to obtain distinctively clear responses in a survey. It limits respondents by providing them with the available choices to choose from

A variable is said to be dichotomous if it has only one two states or categories, for example either male or female or for a coin, either head or tail

State Space

In mathematics a state space is a model of a system related to both the inputs and the outputs of the system

Solution

As such the dichotomous questions to narrow down the entire state space of "flipping a coin and rolling a normal six-sided die" to just 1 outcome are

1. Did the coin land on heads?

2. Is the value on the die odd?

3. Is the value on the die more than 3?

4. Does the value on die equal 1, 2, 5, or 6?

The possible answers to the above questions are yes or no

Possibilities for the coin = heads or tails → possible answers are yes or no

possibilities for the die = 1, 2, 3, 4, 5, or 6

while the possibility of a yes for the die requires as follows

1. Either the die is odd, 1, 3, or 5 or

2 The value of the die is more than 3 which gives 4, 5, or 6

3. Is the value on the die equal 1, 2, 5, or 6

All three questions for the die are required to cover all possible outcomes of 1, 2, 3, 4, 5 and 6 yes or no

Hence there is a possibility to pick the right question to get the same answer for both the coin and the die