Consider the following gambles where, for all, if you lose you get $0.

A: You get $6000 with probability 0.45,

B: You get $3000 with probability 0.90,

C: You get $6000 with probability 0.001,

D: You get $3000 with probability 0.002.

Show that, regardless of your utility for money, you should choose B over A if and only if you choose D over C.