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 $0\mathrm{.}30\mathrm{.}150\mathrm{.}25$

Normal $0\mathrm{.}50\mathrm{.}100\mathrm{.}20$

Recession $?0\mathrm{.}020\mathrm{.}01$

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 $1$ decimal place.$)$

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