SOLUTION: Two cards drawn in succession from a standard deck of cards without replacement.What is the prbability that both cards are greater than 2 and less than 9?

Algebra ->  Probability-and-statistics -> SOLUTION: Two cards drawn in succession from a standard deck of cards without replacement.What is the prbability that both cards are greater than 2 and less than 9?      Log On


   

Question 394923: Two cards drawn in succession from a standard deck of cards without replacement.What is the prbability that both cards are greater than 2 and less than 9?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Two cards drawn in succession from a standard deck of cards without replacement.What is the prbability that both cards are greater than 2 and less than 9?


The probability of drawing the first card as one of these 24


 
          3♥   4♥   5♥   6♥   7♥   8♥   
          3♦   4♦   5♦   6♦   7♦   8♦
          3♠   4♠   5♠   6♠   7♠   8♠  
          3♣   4♣   5♣   6♣   7♣   8♣ 

out of these 52


 
A♥   2♥   3♥   4♥   5♥   6♥   7♥   8♥  9♥  10♥  J♥  Q♥  K♥ 
A♦   2♦   3♦   4♦   5♦   6♦   7♦   8♦  9♦  10♦  J♦  Q♦  K♦
A♠   2♠   3♠   4♠   5♠   6♠   7♠   8♠  9♠  10♠  J♠  Q♠  K♠  
A♣   2♣   3♣   4♣   5♣   6♣   7♣   8♣  9♣  10♣  J♣  Q♣  K♣ 

is 24/52.  

Then having done that, we would draw the second one from 23 out of 51, 
because the one we drew was not replaced, so that's 23/51.

So we multiply (24/52)*(23/51) = 46/221

Edwin