Brain Game: Death by Leon

Today's Brain Game was inspired by an episode of the original Star Trek that I watched again recently - "The Corbomite Maneuver." It's the one where Captain Kirk and his crew are meanaced by first a colorful cube, then by a huge golden chandelier, and finally (gasp) by Clint Howard. Enjoy:

You're holding two six-sided dice decorated with colors on their sides instead of pips. One die has 2 blue sides and 4 red sides, while the other has 1 blue side and 5 red sides. With this in mind:

How many times would you have to roll both dice to exceed a 50% likelihood that you've thrown at least one "double-blue" roll?

Here is the ANSWER.

THE ANSWER:

13 TIMES.

See explanation in the first two comments!