Problem: when a random experiment is conducted , the probability that event a occurs is 1 / 3 . if the random experiment is conducted 5 independent times , what is the probability that event a occurs exactly twice ?
Rationale: one case is : 1 / 3 * 1 / 3 * 2 / 3 * 2 / 3 * 2 / 3 = 2 ^ 3 / 3 ^ 5 we have 5 ! / 2 ! * 3 ! = 10 such cases so , 2 ^ 3 * 10 / 3 ^ 5 = 80 / 243 answer : d .
annotated_formula: subtract(1, divide(const_2, const_3))