Using Probability to Prove Existence

I'm kind of blurring the line between math and philosophy, but I'm hoping I can get some comments on the logic used in the following scenario and if it's a proper application of probability.

A scientist is studying the cause of volcanic eruptions. He is looking at 10 volcanoes that have erupted in the past 50 years. He determines that there is a 20% chance that the cause of each eruption is a dancing pink elephant. Now assuming his assumption is correct, can you use probability to show that it is extremely likely that at least one of the volcanoes erupted because of a pink elephant?

In other words the probability of at least 1 of the volcanoes erupting because of a pink elephant is ( 1 - .2^10) or in other words (99.99998976%).

Is there a flaw in using probability in this way?