You$$re a contestant on the wildly popular $$Deal or No Deal$$ game show with an equal $25\%$ chance at one of four hidden prizes: $$0,$ $$10,000,$ $$50,000$ and $$100,000.$ You can choose to risk it or take a $$deal$$ in which the show$$s banker will pay you $$30,000$ to stop playing and go home as shown in the payoff table below.