An agent has to make a choice between two different gambles:

a) receive 25000 euro with certainty;

b) receive 32000 euro with probability 0.2, 10000 euro with probability 0.7 and 1000 euro with probability 0.1 . The agent is characterized by a power utility function \(u(x)=x^{\gamma}\), with \(\gamma \in(0,1)\), and he is indifferent between two gambles:

c) receive 20.25 euro with certainty;

d) receive 16 euro with probability \(1 / 2\) and 25 euro with probability \(1 / 2\). Determine \(\gamma\) and which of the two gambles a) and b) will be preferred by the agent.