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Students in a fifth grade class are writing reports on famous inventors. Each student may choose one inventor from a list. The teacher does not want any repeats. Maddie chooses first, followed by Zack. $\newline$ Are these two events dependent or independent? $\newline$ Choices: $\newline$ (A) dependent $\newline$ (B) independent

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Identify independent and dependent events

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Q. Students in a fifth grade class are writing reports on famous inventors. Each student may choose one inventor from a list. The teacher does not want any repeats. Maddie chooses first, followed by Zack.

\newline

Are these two events dependent or independent?

\newline

Choices:

\newline

(A) dependent

\newline

(B) independent

Define Events: First, let's define what dependent and independent events are in probability. Independent events are those where the outcome of one event does not affect the outcome of another event. Dependent events are those where the outcome of one event does affect the outcome of the other event. In this scenario, Maddie chooses an inventor first, and Zack chooses second. The teacher does not want any repeats, which means once Maddie chooses an inventor, that inventor is no longer available for Zack to choose.
Events Relationship: Since Maddie's choice directly affects the options available for Zack, the two events are dependent. If Maddie chooses an inventor, Zack cannot choose the same inventor because the teacher wants no repeats. This means that the outcome of Maddie's choice (the inventor she picks) influences the possible outcomes of Zack's choice (which inventors he can pick from).
Example Confirmation: To confirm our reasoning, we can think about an example. If there were only two inventors on the list and Maddie chose one, Zack would only have one inventor left to choose from. This clearly shows that Maddie's choice affects Zack's choice, confirming that the events are dependent.

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