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2. (10 points) Suppose you are playing blackjack against a dealer. In a freshly shuffled deck, what is the probability that e
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Answer #1

To find P(either you or dealer is dealt a blackjack)        
P(either you or dealer is dealt a blackjack)        
     = P(exactly one player gets a blackjack)    (We are assuming both will not get blackjack at the same time)    
         
Number of total deals to the two players         

52C2 x 50C2- 1624350
         
Number of ways exactly one player gets a blackjack         
3c 32      
(i.e., 2C1 = choose which player to give the blackjack,         
4C1 = choose which ace to give them, 16C1 = choose which 10,J,Q,K to give them.         
Then for the other player we either give them two aces from the 3 that are left (3C2),         
give them one ace from the 3 that are left (3C1) and 1 of the 32(32C1) 2-9 cards,         
or give them two non-aces from the 47 non-aces that are left (47C2).)        
         
P(either you or dealer is dealt a blackjack)        
151040 1624350
   = 0.09299       
P(either you or dealer is dealt a blackjack) = 0.09299        

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