Probability that a random bridge board does not contain a sequence?

Question

Two cards with adjacent values and the same suit produce a SEQUENCE. For example, the heart-ten and the heart-jack form a sequence. The order of the values in bridge is $$23456789TJQKA$$

-What is the probability that a random bridge board contains no sequence in any hand ? (That means, for example : If North holds the queen of spades, he neither holds the jack nor the king of spades )

A long time ago, I approached this problem by first determining all possible combinations not containing a sequence (for example kt742) , and then calculate the number of boards from that. I remember that the probability is very low. But there should be a better method, perhaps inclusion-exclusion or something like that.

Answer 1

if i get your question right, an ideal sample set E will be a set of all subsets E={S2,S3,S4,…,S12}

whereas is subset of three serial number s=[n-1,n,n+1]

your sample space for all possible options are equal 2^11 one of these event meet the required criteria which is ‘E' in your case. the probability of having Pr(E=1) = 1/(2^11)

hope it helps