The offer on the table is good. The buyer likes the house, has a lender in mind and wants to move before the school term begins. One sentence in the proposed terms changes the seller's view of the calendar: the buyer needs to sell her own two-bedroom home within sixty days first.
Everyone in this scene is hypothetical. There may be several ways to write that condition into a contract, and the consequences depend on local law and the actual terms. The seller's underlying problem is wider than legal wording. The money she expects from her home now depends on another property finding a buyer, surviving its own transaction and producing funds in time. There are two kitchens, two sets of expectations and at least one deadline. The offer amount shows only one of them.
The sale behind the sale
At first, the chain looks like a simple sequence. The buyer lists her existing home. Someone buys it. She buys the seller's home. The seller receives cash. But part of her down payment is tied up in the two-bedroom. Its old mortgage and selling costs will be paid from that sale first. A lower offer there does not reduce the debt she owes; it reduces the cash available for the next purchase. Then the dates begin to drift. The buyer receives an offer on her own home, but that purchaser has an inspection scheduled. Her lender wants documents that have not arrived. The seller of the larger house must decide whether to keep accepting viewings while the chain waits.
A model that gives each closing an independent chance of success might multiply two numbers and call the result a joint probability. That is a start only if the sales truly do not influence one another. Here they do. A delay in the buyer's sale shortens the time left for the seller's planned move. A changed mortgage rate can affect both the buyer's purchase and the finances of the person buying her old home. If the second purchaser withdraws, the first buyer may still want the new house but can no longer follow the original timetable. The dependency has changed the decision, not merely the arithmetic.
The problem also travels beyond this one chain. When owners must sell and buy in the same market, they are both potential suppliers and potential buyers. Federal Reserve research on the joint buyer-seller problem, using historical Los Angeles data, examines how the difficulty of holding two homes can amplify movement in transaction volumes. That study is not a probability table for today's individual contract. It does show why a home sale and a home purchase cannot always be modeled as separate, unrelated events.
Imagine that the buyer's house attracts no firm offer for three weeks. She can lower her asking price, try to borrow against the home, carry two properties temporarily or abandon the purchase. Carrying two means paying for two loans, insurance policies, tax bills and homes to maintain. Each response costs something and each depends on her circumstances. The original seller has choices too: wait, negotiate a firmer timetable, or consider another buyer whose offer may be lower but less dependent on a chain. The better offer on paper may not be the better route to usable cash by the seller's deadline.