Total Probability of False Detection - 4 Sigma Significance

The following is an exhaustive list of all scenarios to be checked for yielding a significance greater than 4 sigma, but less than 5 sigma.  The total probability from all of these scenarios is less than 6.3 X 10-4, which is the threshold for a significance of 4 sigma.

Scenario resulting in at least 4 sigma significance
Chance Probability Due to Background Fluctuation
7 events in a single bin in 100 second search
8.7 X 10-6
One bin with 4 events in the 1 second search and one bin with 5 or 6 events in the 100 second search
7.6 X 10-6
One bin with 6 events and one bin with 5 or 6 events in the 100 second search
1.96 X 10-5
One bin with 6 events in the 100 second search coincident with a satellite detection
5.3 X 10-7
Total
3.64 X 10-5



Total Probability of False Detection - 3 Sigma Significance

The following is an exhaustive list of all scenarios to be checked for yielding a significance greater than 3 sigma, but less than 4 sigma.  The total probability from all of these scenarios is less than 2.7 X 10-3, which is the threshold for a significance of 3 sigma.

Scenario resulting in at least 3 sigma significance
Chance Probability Due to Background Fluctuation
6 events in a single bin in 100 second search
5.86 X 10-4
4 events in a single bin in 1 second search
2.27 X 10-4
Three bins of 5 events in the 100 second search
3.6 X 10-5
One bin with 5 events in the 100 second search coincident with a satellite detection
3.0 X 10-5
Total
8.79 X 10-4

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