Suppose that each day the price of an investment either increases by $1, holds steady, or decreases by $1 with probabilities 0.3, 0.5, and 0.2 respectively. Assume the price moves independently of the day before.

a. What is the probability that the first day the stock decreases will be one week after purchase?

b. Suppose you have an order to sell the investment on the day it has its second decrease. What is the expected amount of time you will have the investment?

Please explain all parts fully with work and/or formula to show answer was obtained.