I had been solving Bad Luck Island and I wrote this formula for calculating the probability of meeting for example Rock and Paper :
rsp = r + s + p;
rs = r + s;
rp = r + p;
sp = s + p;
P_rp = (r/rsp) * (p/sp) + (p/rsp) * (r/rs);
I figured out that it is wrong, but I want to know why and What am i calculating here ?!
because when i use this formula for all 3 possible meetings , and sum up them , it equals to 1! and I don't know what is the meaning of this formula !!!
( sorry if it is a stupid question! )
I think P_rp = (r*p) / (rsp * (rsp-1))
the editorial says that this will not work !
I just gave this problem a try, my solution to calculate the probability of rock and paper meeting is like this:
first we need to calculate the probabilities of forming each different pair (excluding the similar ones)
P(rp) = r*p/(rsp*(rsp-1)) + p*r/(rsp*(rsp-1))
P(rs) = r*s/(rsp*(rsp-1)) + s*r/(rsp*(rsp-1))
P(sp) = s*p/(rsp*(rsp-1)) + p*s/(rsp*(rsp-1))
Now the probability of meeting rock and paper is : P(rp)/(P(rp)+P(rs)+P(sp)) , because of all possible pairs we need to select only the pairs that have different individuals. You can apply the same for the other two.
thanks , I got my mistake.