Q1. A LED Company manufacturers both green and red light emitting diodes (LED's). When turned off, the red and green LED's look alike. Only when an electrical current is applied, can it be determined whether the LED gives off green or red light. LED's are packaged and shipped in bulk using large cardboard barrels. On a busy production day, one barrel of red LED's was produced. In addition, accidentally, a second barrel was filled with a mixture of LED's, one fourth green and three quarters red. The barrels have no distinguishing markings. Suppose that one of the two barrels is chosen at random, a LED is tested, and it turns out to be RED. What is the probability that it is the barrel with a mixture of green and red LED's?