Question

Two shuffled decks each contain 52 different cards. Lisa randomly chooses one card from the first deck, places it back in the first deck, then randomly chooses a card from the second deck. Which describes the two choices?

A. The choices are dependent because the second choice is influenced by the first choice.

B. The choices are independent because the second choice is not influenced by the first choice.

C. The choices are mutually exclusive because the same card cannot be chosen twice.

D. The choices are complementary because they add up to a specific result.

You can choose the correct answer from these options.

Answer 1

The choices are independent because the second choice is not influenced by the first choice.

Step-by-step explanation:

The correct answer is B. The choices are independent because the second choice is not influenced by the first choice.

When Lisa randomly chooses a card from the first deck and then places it back in the deck before randomly choosing a card from the second deck, each choice is independent of the other. The outcome of the first choice does not affect the probabilities or outcomes of the second choice.

For example, if Lisa chooses a card from the first deck and it is a spade, it does not change the probabilities or available cards for the second choice. Lisa could still choose any of the 52 different cards from the second deck, regardless of the outcome of the first choice.