Consider the following information:

State of Economy Probability of State of Economy Rate of Return if State Occurs

Stock A Stock B Stock C

Boom $\mathrm{.}55\mathrm{.}15\mathrm{.}22\mathrm{.}42$

Bust $\mathrm{.}45\mathrm{.}14\mathrm{.}04\mathrm{.}05$

a$.$

What is the expected return on an equally weighted portfolio of these three stocks? $($Do not round intermediate calculations and enter your answer as a percent rounded to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$ What is the variance of a portfolio invested $24$ percent each in A and B and $52$ percent in C$?($Do not round intermediate calculations and round your answer to $6$ decimal places, e$.$g$.,\mathrm{.}161616.)$