Write the following in math notation.

$1.$ The retum on a stock would be $12\%,45\%,$ or $33\%,$ given that there is a recession, boom economy, and normal economic growth, respectively, There is a $15\%,35\%,$ and $50\%$ probability of a recession, boom economy, and normal economy, respectively.

a$.$ What is the probability of a boom economy?

b$.$ What return would an investor expect for thils stock during a boom economy?

$2.$ John is watching an old game show on television in which the contestant chooses a prize behind curtaln one or curtain two. Behind curteain one is a gas gitit worth $$150$ and behlnd the other is a round$-$the$-$world trip worth $$7,200.$ There is a $75\%$ probabllity of choosing curtaln one.

a$.$ What was the general equation that resulted in the following specific equation: $25=1\mathrm{.}0-75$

b$.$ What was the general equation that resultred in the following spedific equation: $1912\mathrm{.}50=\mathrm{.}25(7200)+\mathrm{.}75(150)$

$3.$ Firm Xs common stock has an expected return of $15$ and a standard deviation of $0\mathrm{.}20.$ Firm Y$\text{'}$s common stock has an expected return of $0\mathrm{.}18$ and a standard deviation of $24.$ The correlation coeficieient between the two firms is $,60.$ You have a portfollo that has $$3000$ invested in Firm $x$ and $$7500$ in Firm $Y.$

a$.$ What was the general equation that resulted in the following specific equation: $286=\frac{3000}{3000+7500}$

b$.$ What was the general equation that resulted in the following specific equation: $\mathrm{.}171=\mathrm{.}714(\mathrm{.}18)+\mathrm{.}286(\mathrm{.}15)$

c$.$ What was the general equation that resulted in the following specilic equation: