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Rob picks a marble at random. Without putting the first marble back, he picks a second marble at random.\newlineAre these two events dependent or independent?\newlineChoices:\newline(A) dependent\newline(B) independent

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Identify independent and dependent eventsright chevron icon

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Q. Rob picks a marble at random. Without putting the first marble back, he picks a second marble at random.\newlineAre these two events dependent or independent?\newlineChoices:\newline(A) dependent\newline(B) independent
  1. Define Events in Probability: First, let's define what independent and dependent events are in probability. Independent events are those where the outcome of one event does not affect the outcome of another. Dependent events are those where the outcome of one event does affect the outcome of the other.
  2. Problem Context: In the context of the problem, Rob picks one marble at random and then, without putting it back, picks a second marble. The outcome of the first pick affects the outcome of the second pick because the first marble is not replaced. This changes the total number of marbles available for the second pick, as well as the probabilities of picking any particular marble on the second pick.
  3. Events Dependency: Since the outcome of the first event (picking the first marble) affects the probabilities in the second event (picking the second marble), the two events are dependent.

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