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?

A. They are dependent because, based on the probability, the first ace was replaced before drawing the second ace.
B. They are dependent because, based on the probability, the first ace was not replaced before drawing the second ace.
C. They are independent because, based on the probability, the first ace was replaced before drawing the second ace.
D. They are independent because, based on the probability, the first ace was not replaced before drawing the second ace.

Answer 1

Option C is right

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

Explanation:

Given that the probability of drawing two aces from a standard deck is 0.0059

If first card is drawn and replaced then this probability would change. By making draws with replacement we make each event independent of the other

Drawing ace in I draw has probability equal to 4/52, when we replace the I card again drawing age has probability equal to same 4/52

So if the two draws are defined as event A and event B, the events are independent

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