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1a) Because the nucleus experiences a nuclear decay from state 1 to state two. After one halftime has passed, there is a 50 percent chance that the nucleus has decayed. After one more halftime, there is a 75 percent change that it has decayed and so on. This means that right after the first decay, there is a higher probability of it decaying again right away, than after several halftimes have passed.
1b) Because the nucleus has the highest probability of emitting a gamma in the positive and negative direction of its orientation. This means that detector 3 will on average receive more gammas than detector 2.
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