high-low stud

hey, i got this question given to me in stats and it's just not making any sense in my head.
in high-low stud a hand counts as low if it consists of five cards, all of different denominations (you are to be given a total of 7 cards because this is 7 card stud) between ace (the lowest) and 8. if the five cards happen to form a stright or a flush, this does not ruin the low, but a pair would. therefore the best low is 5,4,3,2,a (and the second-best is 6,4,3,2,a) the seven-card hand KAA6542 contains a good low, namely 65432A.
-now suppose your first three cards are 8,6,4. what is the probability of completinga low? (hint:you have to improve twice. this could happen in the next two cards, or it could take longer. The best way to think about the different possibilities is to draw a tree diagram. FINAL HINT: the answer is pretty close to 1/2.)


TS Contributor
This problem is more along the lines of "tedious" rather than elegant, but it can be done effectively with a tree diagram.

Starting out with any hand consisting of 8-6-4, assuming a 52-card deck, there are 20 cards remaining that will allow you to continue the "low" and 29 remaining that would not allow you to continue.

Start with the 8-6-4 hand, and make branches that lay out the possible outcomes for the first card, then from those branches, lay out more branches for the second card, and so on....then compute the "conditional" probabilities for each branch or path.

Be careful! Make sure you terminate a branch whenever you are given the second "good" card, or when you are given a third "bad" card - thus making a "low" impossible.

The probability of getting a "low" is 0.543, and the probability of not getting a low is 0.457.

Good luck!
still confused

so I tried to work out this tree diagram but it doen't get the same answer that you gave me, being .543 or close to that. I keep getting 8.7x10^-5 and that's not even close. I don't know what i am doing wrong but could you show me how to do this using a hypergeometric equation or something along those lines, this tree diagram doesn't make sense becuase I don't know how to set it up properly