You and a friend are playing a board game where your income is based on how many squares you progress on a given turn. How far you progress is determined by spinning a dial with values 1-5. Each section on the wheel is proportional to its value (you are twice as likely to get 2 as you are to get 1 and so on).
a. What is the probability you will spin a 3?
b. What is the probability you will spin a 5?
c. If you earn $5 for each square progressed, find the expected value of each spin.
d. Interpret your previous answer.
e. If you earn $5 for each square progressed, find the standard deviation for each spin.
f. If you earn double for an even spin and $7 for each square progressed, find the expected value of each spin.