This is not how you calculate probability. I understand where you get 46%, 6/13. According to you, if there are 2 heroes and 2 SS slots then there is a 100% chance. No, it's 75% chance to see LingLing. LingLing in slot 1 , in slot 2 , in both or none which is 3/4. It is actually less than 1% , around .38% chance to see LingLing.
I assume you used a binomial calculator to calculate this probability. If yes, you got the answer wrong. "Probability" is a value between 0 and 1. In this case the result is 0.38 which means there should be a 38% chance to get at least 1 Ling Ling per refresh.
First you need to find all possible combinations of all heroes showing up in those 6 slots then divide it by all possible outcome. I am not going to explain how combination and permutation work but you can always google it.
Dude, I know how to calculate probabilities... This is a binomial probability and I'm telling you the result is 38%
You don't have to find any combinations/permutations but, since I'm a nice guy I will tell you how to do it, instead of telling you "you can always google it":
. Each slot has a 1/13 probability of any specific hero. So the probability for a specific slot to have Ling Ling is 1/13 = 0.076923 (7.6923%)
. There are 6 slots. The probability of getting Ling Ling in a specific slot is independent from the other slots
. We want to know what is the probability of getting at least one Ling Ling in any of the 6 slots.
. This is a Bernoulli trial with the probability of success (getting Ling Ling) = 0.076923
So, what you have to do is calculate a Binomial Probability with the following parameters:
Probability of success = 0.076923
Number of trials = 6
Number of successes = 1
Now, you can calculate this by hand, or use any of the many available binomial calculators. I used a calculator since it's much easier. Here is the result:
Now, the Binomial Probability is the probability of getting Ling Ling exactly once
in 6 trials, this is not what we want to know but, in you case you need it it's 30.93%
What we want to know is the probability of getting Ling Ling at least once
in 6 trials. This is the Cumulative Probability: P(X >= 1), which is 38%