In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws total a of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is :

The probability that a randomly chosen 5-digit number is made from exactly two digits is :

A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :

Let E^C denote the complement of an event E. Let E₁ , E₂ and E₃ be any pairwise independent events with P(E₁) > 0

and P(E₁ $$ \cap $$ E₂ $$ \cap $$ E₃) = 0.

Then P($$E_2^C \cap E_3^C/{E_1}$$) is equal to :