The reason red was often used at ceremonial and formal events and occasions, is that red carpet was historically and traditionally used to mark the path taken by heads of state and celebrities.

The history of walking on a red carpet in literature appeared in the play ‘Agamemnon’ by Aeschylus, written in 458 BC. When the title character returned from Troy, he is greeted by his wife Clytemnestra who offers him a red path to walk upon. She is quoted as saying, “Now dearest husband, come, step from your chariot. But do not set to earth, my lord, the conquering foot that trod down Troy. Servants, do as you have been bidden: Make haste, carpet his way with crimson tapestries, spread silk before your master’s feet...”.

Other examples in history include orientation carpets in Renaissance paintings that show rugs and carpets, patterned, but with red as the main background color, laid on the steps to a throne, or on a dais where rulers or sacred figures are placed.

Another example, a red carpet was rolled out to a river to welcome the arrival of U.S. President James Monroe in 1821.

Today, film premieres are often laid down with red carpets, and beginning in the 1920s, a red carpet and Hollywood become synonymous. In 1961, the red carpet was introduced at the Academy Awards at the Santa Monica Civic Auditorium. Subsequently, the red carpet became a globally acknowledged focal point for actors and actresses to make a grand entrance.

More Info: en.wikipedia.org