Suppose you won the lottery and had two options: $(1)$ receiving $$0\mathrm{.}5$ million or $(2)$ taking a gamble in which, at the flip of a coin, you receive $$1$ million if a head comes up but receive

zero if a tail comes up$.$

a$.$ What is the expected value of the gamble? Enter your answer in millions. For example, an answer of $$500,000$ should be entered as $0\mathrm{.}5.$ Round your answer to one decimal place.

$

million

b$.$ Would you take the sure $$0\mathrm{.}5$ million or the gamble?

c$.$ If you chose the sure $$0\mathrm{.}5$ million, would that indicate that you are a risk averter or a risk seeker?

d$.$ Suppose the payoff was actually $$0\mathrm{.}5$ million$-$that was the only choice. You now face the choice of investing it in a U$.$S$.$ Treasury bond that will return $$527,500$ at the end of a yea

or a common stock that has a $50-50$ chance of being worthless or worth $$1,150,000$ at the end of the year.

The expected profit on the T$-$bond investment is $$27,500.$ What is the expected dollar profit on the stock investment? Round your answer to the nearest dollar.

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The expected rate of return on the T$-$bond investment is $5\mathrm{.}5\%.$ What is the expected rate of return on the stock investment? Round your answer to the nearest whole number.

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Would you invest in the bond or stock?

T

Exactly how large would the expected profit $($or the expected rate of return$)$ have to be on the stock investment to make you invest in the stock, given the $5\mathrm{.}5\%$ return on the

bond? Round your answer to the nearest whole number. If no exact answer can be obtained, enter $0.$

$\%$