Solve the following problem using Markov Chains.

Consider a retail store that sells a specific product, and its inventory management involves two states: $"$In Stock" and "Out of Stock." The store experiences fluctuations in customer demand, and the inventory level is reviewed periodically. The transition between states depends on the current state and the quantity of products sold or restocked during the review period.

Transition Probabilities:

If the inventory is $"$In Stock," there is a $90\%$ probability of staying $"$In Stock" and a $10\%$ probability of going "Out of Stock" due to unexpectedly high demand.

If the inventory is "Out of Stock," there is an $80\%$ probability of staying "Out of Stock" and a $20\%$ probability of going $"$In Stock" due to a new shipment of products.

Required:

Draw the Markov chain diagram. Use a drawing software for the problem.

What are future states after one iteration? Two? Three?