A street magician asks a volunteer to pick a card, which is put back into the deck at the end of the trick. A

Question

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.

Are these two events dependent or independent?

GPT-5 mini · Answer

Independent.

Reason: “Independent” means knowing the outcome of the first selection does not change the probability distribution for the second. Because the first card was returned to the deck and the deck shuffled, the composition is exactly the same before the second pick. So for any event about the second pick (e.g. picking a particular card or an ace), P(second event | first event) = P(second event). For example, P(second picks a given card) = 1/52 whether or not the first picked that card.

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.

Are these two events dependent or independent?

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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. Are these two events dependent or independent?

All Answers 1

Submit Your Answer

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.

Are these two events dependent or independent?