Final answer:
This question pertains to basic probability concepts, focusing on defining events, calculating probabilities, and determining relationships between events with examples involving cards and dice. The key concepts include understanding sample spaces, events, and probabilities. Options A and B are the correct answer.
Step-by-step explanation:
The student is asking about basic probability concepts and sample spaces in mathematics. Let's define the terms based on the examples given. The sample space (S) is the set of all possible outcomes of a probability experiment. In these examples, the sample spaces include outcomes from drawing cards or rolling dice. An event is a specific set of outcomes from the sample space that shares a particular property, denoted by letters like A or B. The probability of an event (P(A)) is a measure of how likely it is to occur, with a range between 0 and 1, where 0 indicates impossibility and 1 indicates certainty.
Example calculations:
- The event A (even numbers less than 20) would include {2, 4, 6, ..., 18}, and event B (numbers greater than 13) includes {14, 15, ..., 19}.
- The probability of an event A is calculated by dividing the number of favorable outcomes by the total number of outcomes in the sample space.
- The conjunction of A AND B consists of numbers that are both even and greater than 13, e.g., {14, 16, 18}.
- Tree diagrams and Venn diagrams can be used to visually represent these probability concepts and events.
When we consider multiple events, we look at the intersection (AND) of these events to find outcomes that belong to both, and the union (OR) to find outcomes that belong to either one event or the other, or both.