A coin is tossed until a head appears or it has been tossed thrice. Given that head doesn’t appear on the first toss, the probability that coin tossed thrice is

Box-I contains 3 cards bearing numbers 1, 2, 3 , Box II contains 5 cards bearing numbers 1 , 2, 3, 4, 5 and Box III contains 7 cards bearing numbers 1, 2, 3, 4, 5, 6, 7. One card is drawn at random from each of the boxes. If $$x_i$$ be the number on the card drawn from the $$i$$ th box, $$i=1,2,3$$, then the probability that $$x_1+x_2+x_3$$ is odd is equal to

The range of a random variable $$X$$ is $$\{1,2,3, \ldots\}$$ and $$P(X=x)=\frac{C^x}{x !}$$. for $$x=1,2,3$$, ... Then, the value of $$C$$ is

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has 62.5% chance of winning the game. Suppose this coin is tossed 5 times, then the probability of getting exactly 3 head is