I need some explanation

Question 6: Throughout this question (and all its parts), assume that you have a logarithmic utility function U( W J = In[ W i (where \"W" is your wealth in different scenarios]. 3) bl d} Suppose your currentwealth is $5,000, and you nd yourself in a situation in which there is a 50,?50 chance of either winning or losing $1,000. lfyou can buy insurance that completely removes the risk for a fee of $125, will you buy it or take a gamble? Show full workings. Suppose you accept the gamble from Part a] (Le. you do not purchase insurance) and lose, so that your wealth is reduced to $4,000. Would you gamble again for a second time (assuming your preferences remain the same)? Suppose your initial wealth Is $10,000 instead, but as in Part a} you face a 5050 chance of winning or losing 51,000. How much would you be willing to pay for insurance to eliminate the risk? Show full workings. If you are exposed to a 501'50 chance of gaining or losing $1,000 and insurance that removes the risk costs $500, at what level of initial wealth will you be indifferent between taking the gamble and paying for the insurance? Show full workings