Suppose that we have 10 000 spin-1/2 particles, which are either spin up or spin down. Thermal agitation causes them to flip around, so that any one particle spends roughly half the time up and half down. On average, at any instant there will be 5000 up and 5000 down.
(a) What is the standard deviation for fluctuations around this value?
(b) What is the probability that at a given instant there are exactly 4900 up and 5100 down?
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