In December 1995, Chuck Noland (Tom Hanks) is a time-obsessed systems engineer, who travels worldwide resolving productivity problems at FedEx depots. He is in a long-term relationship with Kelly Frears (Helen Hunt), with whom he lives in Memphis, Tennessee. Although the couple wants to get married, Chuck's busy schedule interferes with their relationship. A Christmas with relatives is interrupted when Chuck is summoned to resolve a problem in Malaysia. While flying through a violent storm, his plane crashes into the Pacific Ocean. Chuck escapes the sinking plane and is saved by an inflatable life-raft but loses the raft's emergency locator transmitter. He clings to the life-raft, loses consciousness, and floats all night before being washed up on an island. After he awakens, he explores the island and soon discovers that it is uninhabited.
Several FedEx packages from the crashed plane wash up on the shore, as well as the corpse of one of the pilots, which he buries. He initially tries to signal for rescue and makes an escape attempt with the remnants of his life-raft but cannot pass the powerful surf and the coral reefs surrounding the island. He searches for food, water, shelter, and opens the packages, finding a number of potentially useful items. He leaves one package, with a pair of angel wings stenciled on it, unopened. During a first attempt to make fire, Chuck receives a deep wound to his hand. In anger and pain, he throws several objects, including a Wilson volleyball from one of the packages. A short time later he draws a face in the bloody hand print on the ball, names it Wilson, and begins talking to it. One night, Chuck calculates that in order for the rescue workers to find the site of the plane crash, they'll have to search an area twice the size of Texas, making him doubtful he will ever be found.
Four years later, Chuck is dramatically thinner, bearded, with longer hair, and wearing a loincloth. He has become adept at spearing fish and making fires. He also has regular conversations and arguments with Wilson, his volleyball friend which has become his only means of socialization. A large section from a portable toilet washes up on the island; Chuck uses it as a sail in the construction of a raft. After spending some time building and stocking the raft and deciding when the weather conditions will be optimal (using an analemma he has created in his cave to monitor the time of year), he launches, using the sail to overcome the powerful surf. After some time on the ocean, a storm nearly tears his raft apart. The following day, Wilson falls from the raft and is cast away into the ocean, leaving Chuck crying and overwhelmed by loneliness. Later, a passing cargo ship finds him, drifting.
Upon returning to civilization, Chuck learns that he has long been given up for dead; his family and acquaintances have held a funeral, and Kelly has since married Chuck's one-time endodontist and has a daughter. After reuniting with Kelly, the pair profess their love for each other but, realizing they can't be together because of her commitment to her new family (and also remembering that Chuck wasn't there for her last time), they sadly part. Kelly gives Chuck the keys to the car they once shared.
Sometime later, after buying a new volleyball, Chuck travels to Canadian, Texas to return the unopened FedEx package with the angel wings to its sender, a woman named Bettina Peterson. The house at the address is empty, so he leaves the package at the door with a note saying that the package saved his life. He departs and stops at a remote crossroads. A friendly woman (Lari White) passing by in a pickup truck stops to explain where each road leads. As she drives away, Chuck notices the angel wings on the back of her truck is identical to the one on the parcel. As Chuck is left standing at the crossroads he looks down each road, then smiles faintly as he looks in the direction of the woman's truck.

Question: Which package does Chuck leave unopened?
Answer: A package with a pair of angel wings stenciled on it.
Alternative answer: The one with angel wings on it