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Two cards are drawn from a standard deck of cards.

Part A: If they are drawn with replacement, what is the probability that both cards are 2s? Show your work. 

Part B: If they are drawn without replacement, what is the probability that the first card is a club and the second card is a spade? Show your work. 

Part C: Which of the two scenarios in Part A or Part B represents dependent events? Explain your answer using complete sentences. Show your work. 

davidgba64  Dec 7, 2017
 #1
avatar+86939 
+2

A     ....since we can replace the cards....the probability that that they are both 2's is just

 

(4/52) * (4/52)  =  1/13 * 1/13  =   1/169

 

 

B......we are drawing without replacing....

 

First card a club / Second card a spade (given that the first card is a club) =

(13/52) (13/51)  =  (1/4) * (13/51)  =  13 / 204

 

 

 

C  The second is the dependent event .  We have the same probability for drawing a 2 both times when we replace the cards.  But without replacement, the probability on the second draw can be different.  For instance.....if we  draw a spade on the frist draw....the probability of drawing a spade on the second draw would be different  = 12/51  = 4/13. So the second draw probability depends on the first draw.

 

 

cool cool cool

CPhill  Dec 7, 2017
 #2
avatar+24 
+1

genius.

davidgba64  Dec 7, 2017
 #3
avatar+86939 
0

LOL!!!!....not really a genius....in fact, these probability problems give many of us trouble....including me....!!!

 

 

cool cool cool

CPhill  Dec 7, 2017

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