Final answer:
The answer to the student's question is option (b) x is an even number, which is an open statement. An open statement includes a variable and its truth value can change. The other options are closed statements with fixed truth values.
Step-by-step explanation:
An open statement is a statement that includes a variable and can be true or false depending on the value of the variable. In the provided options, (b) x is an even number is an open statement because whether it is true or false depends on the value assigned to x.
The other statements are closed because they are either always true or always false without any variables.
To define the sample space, events, and probability in a mathematical problem:
- The sample space (S) is the set of all possible outcomes. In one of the problems, the sample space S can be described as the whole numbers starting at one and less than 20.
- An event is a set of outcomes from the sample space that we are interested in. Event A could be the even numbers within the sample space, and Event B could be numbers greater than 13.
- To find the probability of an event, such as P(A), you calculate the ratio of the number of favorable outcomes (the elements in event A) to the total number of outcomes in the sample space.
- To find the intersection of two events, such as A AND B, you determine the elements that are common to both Event A and Event B.
- Probability of the intersection (P(A AND B)) is found by dividing the number of elements in the intersection by the total number of outcomes in the sample space.