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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 10s? Show your work. (1 point)

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 diamond? Show your work. (1 point)

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. (2 points)

Guest Apr 4, 2018
 #1
avatar+90968 
+1

A)

 

We have 4  10s......so  if we have replacement....the probability of  drawing a 10 on each draw is the same  =  4/52

 

So....

P (Two 10s with replacement)   =   4/52  * 4/52   =    1/13  * 1/13      = 1/169

 

 

B )  Without replacement we have   4/52  of drawing a 10 on the first draw and  (3/51)  of drawing a 10 on the second draw

So.....this probability  =  4/52  *  3/51    =   (1/13) * (1/17)  =    1/ 221 

 

 

C) The second event is dependent.  If we   don't draw a 10 on the first draw, the probability of drawing a 10  on the second draw is different  = 4/ 51.   In the first scenario, the probability of drawing a 10 is the same on both draws. Thus, it is independent  - one draw does not affect the other.

 

 

 

cool cool cool

CPhill  Apr 4, 2018

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