Suppose Nick behaves according to Expected Utility theory. That is, when faced with the gamble Win in $x with probability p & win $y with probability q, he assigns a value p.u(W+x)+q.u(W+y) to that gamble.

Assume u(1000)=0 & existing wealth W=1000. Nick prefers $3000 for sure to the gamble ($4000,0.8; $0,0.2). Predict which one he will choose when he is offered the following 2 options: ($4000,0.2; $0,0.8) & ($3000,0.25; $0,0.75).

Can you explain the answer with more detail.