A total of 8 neutrino “events” (like the Supernova SN1987a explosion) were glean

Question

A total of 8 neutrino “events” (like the Supernova SN1987a explosion) were gleaned from the Homestake neutrino detector located in a salt mine near Cleveland (https://en.wikipedia.org/wiki/Homestake_experiment)
(a) If the average number of “background" neutrinos observed per day is known to be 2, calculate the probability that 8 or more such background events will be detected in one day.
(b) If the average number of “background" neutrinos observed per day is known to be 2, calculate the probability that 8 or more such background events will be detected in a 4-hour period.
(c) Based on your answers to parts (a) and (b): Should the experimenters (call them Team A) who observe 8 or more events in a day publish their results as a “discovery," or simply attribute these “events" to a fluctuation in the background rate? If Team B observes 8 or more events in a 4-hour period, is this a discovery, or a likely fluctuation?

Explanation / Answer

(1) average number of “background" neutrinos observed per day = 2 per day

Pr(X >= 8 ; 2) = e- X/X! where X > 8,9....

by poisson table

Pr(X >= 8 ; 2) = 0.0011

so with this probability it means it will happen in 11 times in 10000 days so it can be said a fluctuation not a disccovery.

(b)

average number of “background" neutrinos observed per day = 2 per day

so average number of “background" neutrinos observed per day = 2 * 1/6 = 1/3 per 4 hour

Pr(X >= 8 ; 1/3) = e- X/X! where X > 8,9....

by poisson table

Pr(X >= 8 ; 1/3) = 2.81 x 10-9

so with this probability it means it will happen once in 0.1 million years so surely it is a discovery not a fluctuation.

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