A merchant is considering a purchase of autographed sports memorabilia for resale to collectors. The probabilities of various possible incomes from reselling these collectibles are estimated in the following table:

The merchant believes that, in order to make this purchase worthwhile, the expected profit must be at least \(\$ 200\). Should the collectibles be purchased if the cost is \(\$ 500\) ?

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Income $1,000 $800 $500 $200 Probability 0.12 0.38 0.45 0.05