A six faced fair dice is thrown until $$1$$ comes, then the probability that $$1$$ comes in even no. of trials is

If three distinct numbers are chosen randomly from the first $$100$$ natural numbers, then the probability that all three of them are divisible by both $$2$$ and $$3$$ is

Two numbers are selected randomly from the set $$S = \left\{ {1,2,3,4,5,6} \right\}$$ without replacement one by one. The probability that minimum of the two numbers is less than $$4$$ is

If $$P\left( B \right) = {3 \over 4},P\left( {A \cap B \cap \overline C } \right) = {1 \over 3}$$ and
$$P\left( {\overline A \cap B \cap \overline C } \right) = {1 \over 3},\,\,$$ then $$P\left( {B \cap C} \right)$$ is