Gamble A results in $10 with probability 0.4 and $30 with probability 0.6. Gamble B results in $20 with probability 1. If an individual prefers Gamble A to Gamble B, the independence axiom implies that he prefers Gamble C that gives $0 with probability 0.5, $10 with probability 0.2 and $30 with probability 0.3 to Gamble D that results in $20 with probability 0.5 and $0 with probability 0.5.
Answer the following statement true (T) or false (F)
True
Rationale: Let Gamble E be defined as getting $0 with probability 1. Then Gamble C is the even mixture of Gamble A and Gamble E and Gamble D is the even mixture of Gambles B and E. The independence axiom then applies.
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