An analyst has predicted the following returns for Stock A and Stock B in three possible states of the economy.

State Probability A B

Boom $0\mathrm{.}310\mathrm{.}250\mathrm{.}29$

Normal $0\mathrm{.}490\mathrm{.}210\mathrm{.}23$

Recession $?0\mathrm{.}150\mathrm{.}15$

a$.$ What is the probability of a recession? $($Round your answer to $2$ decimal places.$)$

b$.$ Calculate the expected return for Stock A and Stock B$.($Round your answers to $2$ decimal places.$)$

c$.$ Calculate the expected return for a portfolio that is invested $45\%$ in A and $55\%$ in B$.($Round your answer to $2$ decimal places.$)$