Cart abandonment is a major concern for e-commerce companies in which customers add products to their e-commerce shopping cart but fail to complete the purchase. The states of the cart abandonment and description are given in Table 1. Table 1 State and State Description (estimated based on daily basis)

State	Description
1	Less than 5% abandonment
2	Between 5% and 10% abandonment
3	Between 10% and 15% abandonment
4	Between 15% and 20% abandonment
5	Between 20% and 25% abandonment

The state transition matrix is given in Table 2.

Table 2 State Transition Matrix

	1	2	3	4	5
1	0.80	0.20	0	0	0
2	0.10	0.70	0.20	0	0
3	0.05	0.10	0.65	0.10	0.10
4	0	0.10	0.30	0.50	0.10
5	0	0	0.30	0.40	0.30

Question 1 In the current period cart abandonment is 7%, calculate the expected duration it takes to reach 22% cart abandonment.

Question 2 On day 1, 11% carts are abandoned, what is the probability that on day 3 (d+2) the proportion of cart abandoned is 24%.

Question 3 In the long run (steady state) calculate the probability that the cart abandonment is between 20% and 25%.