The question is "There are 3 uranium atoms held together in a group by a special nuclear force. In any 1 second, each uranium atom can emit any number of photons ranging from 0 up to innity according to the Poisson distribution. Suppose the mean photon emissions are 1, 1.5 and 2 for the 1st, 2nd and 3rd uranium atom, repectively. Assume that the photon emissions from the 3 urnaium atoms are independent of each other. If there are more than 2 photon emissions in 1 second from this group of 3 uranium atoms, then the group will disintegrate. Suppose the uranium group is holding at this moment. Calculate the probability that this uranium group will disintegrate within the next second.

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I am confusing if Poisson distribution can search for the probability of a non-integer event. Here's my though, I first try to combine three independent variables to 1 variable Z~ Poisson (4.5), where I use the equation of P(>2)=1- P(Z=2)-P(Z=1)-P(Z=0). However, the combination of photon numbers could also be 1.5 which cannot be solved by P(Z=1.5). I attempt to raise the unit to 2 seconds, yet it cannot be done as the question is asking on a second basis. May I know how to solve this question?