What's the property that justifies this statement ?

Since each trial has the same probability of success, 

Let, Xi=1 if the ith trial is a success (0 otherwise). Then, X=∑3i=1XiX=∑i=13Xi, 

and E[X]=E[∑3i=1Xi]=∑3i=1E[Xi]=∑3i=1p=3p=1.8E[X]=E[∑i=13Xi]=∑i=13E[Xi]=∑i=13p=3p=1.8

So, p=0.6p=0.6, and P{X=3}=0.63P{X=3}=0.63

I thought what I did was sound, but the textbook says the answer to (a) is 0.60.6 and (b) is 00.

Their reasoning (for (a)) is as follows: