In a certain random experiment, exactly one of the outcomes A, B, and T will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and T will occur twice?
Choose the most appropriate option: A) 5/243 B) 1/12 C) 10/81 D) 1/6 E) 16/81
Number of ways in which a group of 2A,2B,2T can be formed in any order = 6!/(2!*2!*2!) [ formula for total of 6 items with 2 each of similar kind)   Total number of ways in which the die can be thrown independently = _ _ _ _ _ _ ; there are 6 places .First can be filled in 3 different ways A/B/T; Second in 3 diff ways again and so on.   So total number of ways = 3X3X3X3X3X3 = 3^6   There fore probability = 6!/(2!x2!x2!) by 3^6 = 90/3^6 = 10/81 Answer 10/81
<result>C</result>
In a certain random experiment, exactly one of the outcomes A, B, and T will occur. In each random experiment, the probability that outcome A will occur is 1/3 , and the probability that outcome B will occur is 1/3. What is the probability that when the random experiment is conducted 6 independent times, each of outcomes A, B, and T will occur twice?