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Identify whether the following situations is dependent or independent. You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die show a one.

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Identify independent and dependent events

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Q. Identify whether the following situations is dependent or independent. You flip a coin and then roll a fair six-sided die. The coin lands heads-up and the die show a one.

Understand scenario: Step $1$ : Understand the scenario. $\newline$ We have two events: flipping a coin and rolling a die. We need to check if the outcome of one affects the other.
Analyze events: Step $2$ : Analyze the events. $\newline$ The coin flip results in heads or tails, and the die roll results in numbers from $1$ to $6$ . These two events do not influence each other; the result of the coin flip doesn't change the probabilities of the die roll outcomes.
Define events: Step $3$ : Define dependent and independent events. $\newline$ Events are independent if the outcome of one does not affect the outcome of the other. They are dependent if the outcome of one event affects the outcome of the other.
Apply definition: Step $4$ : Apply the definition to the scenario. $\newline$ Since the coin flip and the die roll do not influence each other, they are independent events.

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