We throw a die repeatedly and we stop when the outcome is either five or six.

(i) What is the probability that k throws will be needed and the outcome of the kth throw is six?

(ii) What is the probability that throws are terminated when a five occurs?

(iii) If we know that at least three throws of the die will be needed, what is the probability that the series ends with a five?

(iv) If we know that the series ends with a five, what is the probability that at least three throws of the die will be needed?