How do I find the probability that one of my probabilities will occur?

Question

I've been struggling with this problem all day. I've got a set of events each with probabilities.

{'Bob': 0.82,
 'Derek': 0.69,
 'Sarah': 0.91,
 'Peter': 0.46,
 'Amy': 0.62,
 'Ryan': 0.7}

I created a list of outcomes that are not conditional. For example P(Derek) and P(Amy), which is the intersection, so I multiply.

P(Derek ∩ Amy) = .82 *.62 = 0.42779999999999996

Here is my full list of outcomes I'm interested in:

{('Derek', 'Amy'): 0.42779999999999996,
 ('Bob', 'Peter', 'Amy'): 0.233864,
 ('Bob', 'Ryan', 'Sarah'): 0.52234,
('Bob', 'Ryan', 'Amy'): 0.35588,
...
('Ryan', 'Sarah', 'Derek'): 0.43953}

None of my outcomes are duplicates nor are they supersets.I want to find the probability that exactly one of these occurs.

Is this the correct method?

prob = 1.0

for event in events:
    prob *= (1.0 - event)

probability_of_one_event = 1 - prob
print("Probability of at one event is", probability_of_one_event)

I'm asking because the number I'm getting is 99%, which seems too high. I need help thinking about this. Thanks!