$1)$ problem $11$: you have been given $$1,000$ and are to choose between

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A: $($$$1,000,\mathrm{.}50)$ a $50\%$ probability of winning $$1,000$

B: $($$$500)$ a sure win of $$500$

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problem $12$: you have been given $$2,000$ and are to choose between

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C: $($$$-1,000,\mathrm{.}50),$ a $50\%$ probability of losing $$1,000$

D: $($$$-500)$ a sure loss of $$500$

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First, state the results Kahneman and Tversky obtained$$ when they ran these choices by participants, i$.$e$.$ what were the percentages of people who chose A and B in problem $11$ and C and D in problem $12$ in their experiments? $(15$ marks$)$

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Then, explain why these results may point to people$$s tendency to fail to integrate the payoffs, that is$,$ initial endowment plus the outcome of their choice between$$ A and B or C and D$,$ in each case $(20$ marks$).$ If an individual exhibits mental accounting of the form that we observe in these experiments, how might his$/$her attitudes towards loss$-$making stock investments differ from profitable ones in real life? Briefly comment