Subjects probability

Dependent Events 971C17

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1. **State the problem:** We need to identify which events are dependent among the given scenarios. 2. **Definition:** Events are dependent if the outcome or occurrence of the first event affects the probability of the second event. 3. **Analyze each scenario:** - Scenario 1: You select a blue marble, return it, then select a red marble. Since the marble is returned, the second draw is unaffected by the first. These events are independent. - Scenario 2: You choose a red card and keep it, then choose another red card. Since the first card is not replaced, the total number of cards changes, affecting the probability of the second event. These events are dependent. - Scenario 3: A boy rolls a 5, then rolls again. Each roll is independent because the die is fair and rolls do not affect each other. - Scenario 4: The first child is a boy, and the second child is also a boy. Assuming gender of each child is independent, these events are independent. 4. **Conclusion:** Only scenario 2 describes dependent events because the first event affects the second. **Final answer:** The events in scenario 2 are dependent.