To create scenarios for events A and B using 6 different-color marbles, we can define event A and event B in such a way that they cover all possible outcomes when selecting the marbles.
Scenario for Event A:
Event A: Selecting at least one marble of a specific color, say red, from the 6 different-color marbles.
Result of Event A: The outcome of event A occurs if at least one red marble is selected from the group of 6 marbles, which includes colors red, blue, green, yellow, orange, and purple.
Scenario for Event B:
Event B: Selecting all 6 marbles, without any restrictions on color.
Result of Event B: The outcome of event B occurs if all 6 marbles are selected from the group of marbles includes red, blue, green, yellow, orange, and purple.
Probability and Relationship:
Since selecting all 6 marbles guarantees that at least one red marble (or any other color) will be included in the selection, we have:
- \( P(A \text{ and } B) = 1 \) This means that the occurrence of event B (selecting all 6 marbles) guarantees the occurrence of event A (redundantly ensuring at least one red marble is selected).
Independence or Dependence:
- Events A and B are dependent events because the occurrence of event B directly affects the outcome of event A. Selecting all marbles ensures that at least one red marble will be selected, so the probability of event A is influenced by the occurrence of event B.
Summary:
- Event A: At least one red marble is selected.
- Event B: All marbles are selected.
- Relationship: \( P(A \text{ and } B) = 1 \) indicates events A and B are dependent events.