Marley is looking to purchase a house. The list price for the home is $600,000, but he believes purchasing this home right now is worth $700,000 to him (this combines both his belief that the actual home value is higher than $600,000 and his time savings from not having to continue searching). His real estate agent has reached out to the seller and found out that there is currently one other interested buyer. He has also learned that the seller will not entertain any offer of less than $550,000. The agent believes the following about the other buyer's type of offer:

20% probability of no offer (i.e., $0)

20% probability of a cash offer

60% probability of a bank loan offer

If the other buyer's offer is cash, then there is a 75% chance it will be exactly $600,000 and a 25% chance it will be $620,000. If the other buyer obtains a bank loan, then the offer will be $600,000 with 20% probability, $640,000 with 30% probability, and $660,000 with 50% probability.

(1) If the other buyer's offer is cash, what is the expected amount of the offer?