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Lets say I have a low intensity light source emitting one photon per second. Can you theoretically determine the probability of that photon passing through the left or right slit?

For example, 10 photons are emitted and I would like to calculate the probability of all ten passing through the right slit. Can this be done through normal statistical methods? If so, that would tell me that the probability would be $0.5^{10}$.

Is this a correct way of thinking about it? I understand that you can't actually detect which slit it passes through so this is a purely theoretical question.

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Your question makes sense only if there is some kind of detector positioned at the slits to check which slit the photon passes through (but then you will not get interference phenomenon). If the photon emission mechanism is symmetric w.r.t. positioning of the two slits and if we consider only those photons that are not absorbed by the barrier into which those slits have been cut, then the probability that a photon will be registered at (say) right slit is indeed 0.5, just by symmetry considerations. Then the probability of detecting 10 photons at the same slit is $0.5^{10}$, given that only those photons not absorbed by the barrier are being considered.

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