If you have a 1 in a thousand chance of winning $400, but 999 out of a thousand times you win nothing, what is your expected payoff​

Answer:$0.4Step-by-step explanation:Let [tex]P_{w}[/tex] be the probability of winning.Let [tex]P_{l}[/tex] be the probability of loosing.Given that we win once in thousand times.So,[tex]P_{w}=\frac{1}{1000}[/tex]Since [tex]P_{w}+P_{l}=1[/tex][tex]P_{l}=1-P_{w}=1-\frac{1}{1000}=\frac{999}{1000}[/tex]Since we win noting if we loose,expected payoff is product of probability of winning and the prize.Let [tex]pr[/tex] be the prize.Given,[tex]pr=400[/tex]Expected payoff is [tex]pr\times P_{w}=400\times \frac{1}{1000} =0.4[/tex]So,$[tex]0.4[/tex] is the expected payoff each time.