Donor-Participants species probability

[papori]

Hi all,
We are doing a microbiome study with FMT (Fecal Microbiota transplant), and I have a statistic question about something we found.

Background
In the experiment there are 2 donors and 11 recipients.
Donor 1 group are 6 participants
Donor 2 group are 5 participants

Result of FMT
In Donor 1 group we have 3 responders, and 3 non responders
In Donor 2 group we have 0 responders, and 5 non responders

We found that there is only one species that is in Donor 1 and in the 3 responders, but not found in the rest.
We suspect that this species can be a marker for matching Donor-Participant for being a responder.
We have 200 species in all the samples together.

Question
I would like to calculate the probability for this, and I believe Bayes probability is the way.
I think that I know how to ask the question, but not to do the calculation and I will appreciate your help:

What is the likelihood to be this species that found only in Donor 1 and in his responders, when I have only 3 responders out of 11 participants and 2 Donors?

Thanks for the reading, and I hope to understand it ��