Consider a system A consisting of a spin 1/2 having magnetic moment ##\mu_0##,
and another system A' consisting of 3 spins 1/2 each having magnetic moment ##\mu_0##.
Both systems are located in the same magnetic field B .
The systems are placed in contact with each other so that they are free to exchange energy.
Suppose that, when the moment of A points up (i.e., when A is in its + state), two o f the
moments o f A' point up and one of them points down.
Count the total number of states accessible to the combined system A + A ' w hen the moment o f A points up, and when it points down. Hence calculate the ratio P_/P+, where
P_ is the probability that the moment of A points down and P+ is the probability that it points up.
Assume that the total system A + A ' is isolated.
The Attempt at a Solution
I feel like my answer this this is waaaay off just because the way I'm thinking about this makes it seem too easy.
It feels like the probability for A's moment to be + is 3/4, as just from reading previous examples in the book all they seem to note is that it would be the number of + spins over the total number of spins. The - probability would be similar.
What's telling me something is wrong about this is when I generalize to N number of spins in A', I don't get answers that seem right when using this logic.
Is it really this easy or am I missing something???