The median percentage of the Transgender Community in the world is 1%
1% of 8 billion is 80 million
This means that the Odds of even meeting or knowing a Transgender person is 0.000125% (1)

According to a study conducted by researchers at the University of Oxford, the average person has about 536 social interactions per day
Now with all of the above said the chance of interacting with a transgender person worldwide is a probability of 0.37%.

Now knowing I could have messed up on my math. I am going to give you the basic odds of meeting a Transgender person in a bathroom. This number can be as high as 0.000000625% chance.
What does that mean in the number of people? 1 in 1,600,000 apx.

This means we need to look at the 536 social interactions closer.

Social interaction refers to the ways in which people communicate and interact with one another in a social context. It includes verbal and nonverbal communication, such as talking, listening, gesturing, and body language, as well as shared activities and experiences, such as playing games, working together, or participating in cultural events.

Social interaction is an essential aspect of human life, as it helps us to form social connections, build relationships, and establish a sense of belonging and identity. It allows us to share information, express emotions, and learn from others, as well as to develop social skills and behaviors that are important for our personal and professional lives.

Examples of social interactions include conversations with friends or colleagues, attending social events such as parties or gatherings, playing sports or games with others, participating in group projects or activities, and interacting with strangers in public places.

That means unless you talk to a person or interact with that person you are not having a social interaction. So in the case of meeting a Transgender person in a bathroom is greatly reduced unless you talk to a total of 536 people, in a given bathroom.

I am not going to give you the complete context of the question as it is not needed to prove the point that meeting a Transgender person in a bathroom is extremely rare. As I am sure you are not going to have 536 interactions in one day in a bathroom. So thank you J for the question and I hope this helps you understand my answer to you. (Gawd I hate maths)

1. these numbers can fluctuate depending on parts of the world, specific communities, employment, inclusion in the LGBT+ community, etc.