Let's consider a scenario where we have 6 different-color marbles: Red, Blue, Green, Yellow, Orange, and Purple. We randomly select 6 marbles, each of a different color.
Event A:
Scenario for Event A: Let's define event A as selecting the Red marble and the Blue marble among the 6 different-color marbles. For this event, we have two specific outcomes: selecting the Red marble (R) and the Blue marble (B).
Result of Event A: The outcome of event A is {R, B}.
Event B:
Scenario for Event B: Now, let's define event B as selecting a marble that is Yellow or Green among the 6 different-color marbles. For this event, we can have two outcomes as well: selecting the Yellow marble (Y) or the Green marble (G).
Result of Event B: The outcomes of event B are {Y} and {G}.
Probability Calculation:
Now, if we want to calculate the intersection probability, \( P(A \text{ and } B) = 130 \), we can think of \( P(A) \) and \( P(B) \):
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P(A): The probability of selecting the Red and Blue marble together. Since there are 6 marbles and the selection is random, the probability of selecting the specific colors can be calculated based on combinations.
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P(B): The probability of selecting either the Yellow or Green marble from the total also needs to consider how many combinations yield that outcome.
To simplify, let's assume we are not using numerical values directly.
Independence or Dependence:
To determine if events A and B are independent, we look at the occurrence of one event affecting the occurrence of the other:
- Events A and B are dependent, because the selection of marbles that constitute one event may affect the number of combinations available for the other event. For example, if the Red and Blue marbles are chosen for event A, the total choices for event B may reduce proportionally, affecting the overall outcome.
Summary:
- Result of Event A: {R, B}
- Result of Event B: {Y} or {G}
- Independence: Events A and B are dependent since the selection of marbles for A affects the possible outcomes for B.
This concludes the analysis of events A and B with the provided conditions.