The probability that an event occurs more than once, not specifically 2, 3, 4 times etc Let's say 100 spam emails are sent out to 200 people.  What is the probability that an individual receives multiple spam emails?
My understanding is that for each email sent out, it would be a 1/200 chance an individual receives a spam email assuming they are sent at random and independent events.  Then because the individuals can work with replacement, the odds of the individual receiving the second email that goes out will also be 1/200. Therefore the odds that an individual receives 2 of the spam emails that are sent out would be (1/200 * 1/200).  However I'm getting confused on how to determine the probability of receiving multiple emails, not specifically two, three, four etc. How do I go about calculating a "more than one" probability? I am believing this is some type of binomial distribution problem, but I do not have a specific number of success cases, just "more than one".
Any help to point me in the right direction?
Edit:
For clarity, I'm using the following to deduce the probability of getting 1 email of the 100 over 200 people:

This comes to roughly 30%, and p(0) is roughly 60%. Is my thought process sound this far? Is the likelihood of receiving multiple email then 70% (1-0.3)?

Ehhh, I was never good at counting but I can give it a shot.  Let me clarify the question prior to providing an answer.
There are 200 people, and 100 spam emails.  Each of the emails is assumed to be sent out to one of the 200 people at random and without concern for if the person has already received an email.  You are interested in knowing the probability that any of the 200 people receives multiple emails, correct?
If I have understood the question, then I think we can apply some basic counting techniques.  Instead of getting the probability we want directly, let's get the probability that all emails are sent to a unique person.  The answer is then the compliment of this event.
Let's start with counting all the ways the 100 emails could be dispersed among the 200 people.  It could be possible (although perhaps improbable) that all 100 emails are sent to the same person.  With this in mind, consider the first email.  To how many people could it be sent?  200.  What about the second email?  To how many people could it be sent? 200.  And so on and so on.  Hence, there are $200^{100}$  possible ways we could dole out these emails.
In how many ways do these emails get sent to a single person (no duplicates).  Again, consider the first email.  We have 200 options.  We select 1 person, leaving us 199 persons left.  We again select 1 of the 199 persons we have not sent an email to, leaving us with 198 options. We do this until we run out of emails to give, so the numerator is $200 \cdot 199 \cdot 198 \cdot \dots \cdot 100 = \dfrac{200!}{100!}$.
The answer should then be
$$ 1- \dfrac{200!/100!}{200^{100}} $$
We can verify this approach gives the correct result with some simulation.  Let's consider a smaller example

set.seed(0)
emails <- 5
persons <- 10

# Compute probability all emails are sent to a single person (no person recieves multiple emails)
prob = gamma(persons+1)/gamma(persons-emails+1) / persons^emails

# Probability we want is the compliment of this event
prob_want = 1-prob
prob_want
#> [1] 0.6976

# Via simulation
sim = replicate(100000, {
  
  # Draw people with replacement.
  x = sample(persons, size=emails, replace=T)
  
  # If we draw fewer unique people than the number of emails, then there is someone who gets more than one email
  length(unique(x)) < emails
  
})


mean(sim)
#> [1] 0.69724

Created on 2021-08-21 by the reprex package (v2.0.1)
