The red rose was the traditional symbol associated with the House of Lancaster.
The red rose became linked with the Lancastrian dynasty through royal badges used by members of the wider Plantagenet family. Its supposed opposition to the white rose of York helped give the fifteenth-century dynastic conflicts their famous name: the Wars of the Roses.
The historical picture is more complicated than the familiar red-versus-white story suggests. Evidence that Lancastrians consistently wore a red rose during the wars is limited, and historians believe the symbolism was strengthened after the conflict. Henry VII, a Lancastrian claimant, later used a Tudor rose combining the red rose of Lancaster with York’s white rose after marrying Elizabeth of York in January 1486.
The red rose is therefore the standard quiz answer, while the white rose belongs to York. Yellow, blue, and white are not the conventional symbols of Lancaster, although red roses later became strongly associated with Lancashire and related institutions.