Let's see if we can pick it apart.
The probability of drawing two cards from a deck and their sum is > 16.
There's a trick here because of Jack, Queen, King also count as 10.
We can have Ace-Ace and Ace-not Ace. To sum over 16 we must have A6, A7, A8, A9, A10, AJ, AQ, AK, or AA.
For 10, J, Q, K we have
For 9, we have
For 8, 7, and 6 we have
Add them up and get
I could easily be over or under counting.
total more than 16 but not blackjack or double ace:
1st card A 2nd card 6, 7, 8, 9 (4/52)x(4/51)
1st card "10" 2nd card 7, 8, 9, "10" (4/52)x(27/51)
1st card 9 2nd card 8, 9, "10", A (4/52)x(27/51)
1st card 8 2nd card 9, "10", A (4/52)x(24/51)
1st card 7 2nd card "10" A (4/52)x(20/51)
1st card 6 2nd card A (4/52)x(5/51)
so probability is:
(4/52)x(4/51) + (4/52)x(27/51) + (4/52)x(27/51) + (4/52)x(24/51) + (4/52)x(20/51) + (4/52)x(5/51)
RonL
Hello, badboychow!
There are: .You draw 2 cards from a deck of 52 cards.
. .
(Assume the face value of an Ace is 11)
Find the expected value.
Double Aces: .There are ways.
Blackjack: .There are ways to get an Ace.
. . . . . and ways to get a card worth 10.
. . So there are: . Blackjacks.
Hence, there are: . 70 ways to win $50.
Sum greater than 16
We can have an Ace (4 choices) and any of 6, 7, 8, or 9 (16 choices).
. . There are: . ways.
We can have a 7 (4 ways) and any "10" (16 ways).
. . There are: . ways.
We can have an 8 (4 ways) and a 9 or a "10" (20 ways).
. . There are" . ways.
We can have two 9's. .There are: . ways.
We can have a 9 (4 ways) and a "10" (16 ways).
. . There are: . ways.
We can have two "10's". .There are: . ways.
Hence, there are: . 398 ways to win $10.
Then there are: . 858 ways to lose $5.
The expected value is: .
. .
Therefore, we can expect to win an average of about $2.41 per game.