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A street magician asks a volunteer to pick a card, which is put back into the deck at the end of the trick. A few minutes later, the magician shuffles the deck and asks a different person to choose a card. $\newline$ 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. A street magician asks a volunteer to pick a card, which is put back into the deck at the end of the trick. A few minutes later, the magician shuffles the deck and asks a different person to choose a card.

\newline

Are these two events dependent or independent?

\newline

Choices:

\newline

(A) dependent

\newline

(B) independent

Understand Definitions: The first step is to understand the definition of independent and dependent events. 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.
Analyze Situation: Next, we analyze the situation described. The volunteer picks a card, and then the card is put back into the deck. This means that the deck is returned to its original state before the second person picks a card.
Deck Reset: Since the card is put back into the deck and the deck is shuffled, the outcome of the first card selection has no effect on the outcome of the second card selection. Each person has the same probability of picking any given card from the deck, regardless of what happened during the previous selection.
Events Independence: Based on the analysis, we can conclude that the two events are independent because the outcome of the first event does not affect the outcome of the second event.

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