1r. the attempt on this page is to show the probabilities of a run (streak) of at least X in length happening at least 1 time in N trials.

It is possible to have more than 1 such streak in N trials that is totally separate from each other.

An error will happen in the code result for more streaks possible. example: run=5, n=20,s=4 will return an error (Error in mruns(5, 20, 0.5, 4) :

The number of streaks(s) must be less than or equal to (<=) maxRun below)

n=20;r=5;

quotient=floor(n/(r+1));

remainder=n%%(r+1)#2,2 and 2 = r

if(remainder==r){

s=quotient+1

}else{

s=quotient

}

print(s)

R code below (needs to be updated as probability distribution of exactly X runs is missing)