Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are 7s? Are these events independent?

A. 3/676 ; no, they are dependent events
B. 1/169 ; yes, they are independent events
C. 2/13 ; yes, they are independent events
D. 1/221 ; no, they are dependent events

Question

Two cards are drawn without replacement from a standard deck of 52 cards. What is the probability that both cards are 7s? Are these events independent?
 
A. 3/676 ; no, they are dependent events 
B. 1/169 ; yes, they are independent events
C. 2/13 ; yes, they are independent events
D. 1/221 ; no, they are dependent events

jskinny0831 · Answer

i got A 3/676 by dividing 1/52 and then dividing that by 7.. am i right?

jskinny0831 · Answer

@Directrix can you help?

directrix · Answer

There are 4 seven cards in the deck.

The probability that the first one is a seven is 4/52.

That is because of the 52 possible outcomes, four are the seven card wanted.

directrix · Answer

On the second draw, there are now 51 cards left in the deck because the first one was not replaced.

directrix · Answer

There are now only 3 seven cards in the remaining 51 cards.

directrix · Answer

The probability of two sevens is:

4/52  *   3/51  =  ?

jskinny0831 · Answer

1/221

jskinny0831 · Answer

so theyre dependent?

directrix · Answer

Because the outcome of the first draw altered the outcome of the drawing of the second seven, yes, the events are dependent.

jskinny0831 · Answer

okok thank you so its definitely D

jskinny0831 · Answer

can you help me with another question

directrix · Answer

You'll need to close this thread and post the next question in a new thread.

jskinny0831 · Answer

yeah i know ill do it now