The correct option that best describes how the federal court system decides which criminal cases to take is:
3. They take cases that are being appealed.
Federal courts, particularly the U.S. Supreme Court, primarily hear cases that are on appeal from lower courts, including state courts and federal district courts. The Supreme Court has the discretion to choose which cases to hear, often focusing on those that involve significant constitutional issues or that resolve disagreements among lower courts.
Option 4 also has a partial truth, as Supreme Court justices play a role in deciding which cases are granted certiorari (i.e., accepted for review). However, the broader process of federal criminal cases generally revolves around appeals to the federal courts.
Options 1 and 2 are not accurate representations of how cases are chosen for federal court. Federal courts do not automatically take cases merely because they have been through state courts or rely solely on grand jury decisions for determining cases to hear.