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Without looking, Zack chooses a colored marble from a mixed bag of marbles, writes down the color, and returns it to the bag. Then, he draws another marble without looking. $\newline$ Are these two events dependent or independent? $\newline$ Choices: $\newline$ (A) dependent $\newline$ (B) independent

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Identify independent and dependent events

Full solution

Q. Without looking, Zack chooses a colored marble from a mixed bag of marbles, writes down the color, and returns it to the bag. Then, he draws another marble without looking.

\newline

Are these two events dependent or independent?

\newline

Choices:

\newline

(A) dependent

\newline

(B) independent

Choose and Record Marble: Zack chooses a marble from the bag, writes down the color, and then returns the marble to the bag. This means that the composition of the bag is the same for the second draw as it was for the first draw. The outcome of the first event does not affect the outcome of the second event because the marble is returned to the bag, restoring the original conditions.
Return Marble to Bag: Since the outcome of the first draw does not affect the outcome of the second draw, the two events are independent. Each draw is a separate event with the same probability distribution as the other draws.

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