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Probability of a Flush Draw with an Inside Straight Draw

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Suppose you are playing Texas holdem and you hold the 8 and 9 of hearts. The flop comes the 3 of hearts, the jack of spades and the Queen of hearts. You now have an inside straight draw (needing a 10 for a straight) and a flush draw (needing a heart for a flush).

a) What is the probability that you hit a straight or a flush on the turn?

b) What is the probability that you hit a flush or a straight on either the turn or the river?

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Solution Summary

This solution calculates the probability of a hitting flush draw with an inside straight draw in the card game Texas Holdem using established theories of probability. The probability that you hit a flush or a straight is determined. The probability that a flush or straight on either the turn or the river is determined.

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a) What is the probability that you hit a straight or a flush on the turn?

There are three non-heart 10's in the deck and 9 remaining hearts so there are 12 cards among the remaining 47 unseen cards that can make you either a straight or a flush on the turn. The probability of making one of these hands on the turn is therefore ...

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