PROBLEMS $-$ Write down the process of calculation clearly. $(40\%)$

$12.$ The rate of return on the common stock of Apple is expected to be $22$ percent in a boom economy and $3$ percent in a recession. The probability of a boom in the following year is $25$ percent. What is the expected return of the common stock? $(7\%)$

$13.$ Following the previous question, what is the standard deviation of the returns on this common stock? $(8\%)$