Hello all,
I am working on probability and specific hands in blackjack.
Phil and Jerry are playing blackjack. Phil is the dealer and they follow standard rules. On the first hand, Jerry gets an 18 (Jack and Eight), but Phil wins with 21 (King and Ace).
What are the odds of Jerry and Phil each getting a queen-ten on the next hand?
Ok, I know that the first number in my work should be 8/48 because there are a total of 8 cards satisfying the condition of being a Queen or a Ten and there are 48 cards left because of two hands being dealt. If we assume they alternate cards between the person receiving and dealer, then the next number should be 7/47 because we have removed either a Queen or a Ten and therefore both numerator and denominator must decrease by one.
Here is where I am perplexed, I thought the next two numbers would be 6/46 and 5/45 for the following:
8/48 x 7/47 x 6/46 x 5/45
However, I have been told that the correct numbers should be: 8/48 x 7/47 x 4/46 x 3/45
I am trying to understand the reasoning of this and believe it may have to do with perhaps the order? or removing the possibility that someone receives both Queens or Tens?
Thanks for any help.
I am working on probability and specific hands in blackjack.
Phil and Jerry are playing blackjack. Phil is the dealer and they follow standard rules. On the first hand, Jerry gets an 18 (Jack and Eight), but Phil wins with 21 (King and Ace).
What are the odds of Jerry and Phil each getting a queen-ten on the next hand?
Ok, I know that the first number in my work should be 8/48 because there are a total of 8 cards satisfying the condition of being a Queen or a Ten and there are 48 cards left because of two hands being dealt. If we assume they alternate cards between the person receiving and dealer, then the next number should be 7/47 because we have removed either a Queen or a Ten and therefore both numerator and denominator must decrease by one.
Here is where I am perplexed, I thought the next two numbers would be 6/46 and 5/45 for the following:
8/48 x 7/47 x 6/46 x 5/45
However, I have been told that the correct numbers should be: 8/48 x 7/47 x 4/46 x 3/45
I am trying to understand the reasoning of this and believe it may have to do with perhaps the order? or removing the possibility that someone receives both Queens or Tens?
Thanks for any help.