Question

The probability of drawing two aces from a standard deck is 0.0059. We know this probability, but we don't know if the first card was replaced. If the two draws are defined as event A and event B, are the events dependent or independent? They are dependent because, based on the probability, the first ace was replaced before drawing the second ace. They are dependent because, based on the probability, the first ace was not replaced before drawing the second ace. They are independent because, based on the probability, the first ace was replaced before drawing the second ace. They are independent because, based on the probability, the first ace was not replaced before drawing the second ace.

Answer 1

Answer:

They are independent because, based on the probability, the first ace was replaced before drawing the second ace.

Step-by-step explanation:

The probability of drawing two aces from a standard deck is 0.0059.

The first card was replaced since the probability of ace  is calculated as:

$\dfrac{4}{52}\times \dfrac{4}{52}=\dfrac{1}{13}\times \dfrac{1}{13}=0.0059$

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Since if the cards were not replaced than the probability of drawing a ace is calculated as:

$\dfrac{4}{52}\times \dfrac{3}{51}=\dfrac{1}{13}\times \dfrac{1}{17}=0.0045$

If the two draws are defined as event A and event B.

then the two events are independent since in replacement the number of cards remain same and we have equal probability i.e. $\dfrac{4}{52}$ of drawing a ace card in the second draw while this will not be the case when the drawing of the second card is done without replacement.

Hence, the answer is:

They are independent because, based on the probability, the first ace was replaced before drawing the second ace.

Answer 2

Event A and event B, then they are independent because, based on the probability, the first ace was replaced before drawing the second ace.