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Karen picks a card at random. Without putting the first card back, she picks a second card at random. $\newline$ 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. Karen picks a card at random. Without putting the first card back, she picks a second card at random.

\newline

Are these two events dependent or independent?

\newline

Choices:

\newline

(A) dependent

\newline

(B) independent

First Event Impact: Karen is picking two cards from a deck without replacement. This means that the outcome of the first event (picking the first card) affects the probability of the second event (picking the second card). Since the first card is not put back into the deck, the total number of cards in the deck is reduced by one, which changes the probabilities for the second draw.
Example Illustration: To illustrate this with an example, if Karen picks a card from a standard deck of $52$ cards, there are $52$ possible outcomes for the first card. If she does not put the card back and picks a second card, there are now only $51$ possible outcomes for the second card. The probability of picking any particular card on the second draw is affected by what happened on the first draw.
Dependent Events: Since the probability of the second event is influenced by the outcome of the first event, the two events are dependent.

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