Two coins are tossed. Let $A$ be the event that the first coin shows a head and $B$ be the event that the second coin shows a tail. The two events $A$ and $B$ are:

If $S$ is the sample space of a random experiment $\xi$ and $P$ is a probability function defined on the power set $\mathcal{P}(S)$ of $S$,then which one of the following is not satisfied by $P$?
$(i)$ $P(\phi) = 0$
(ii) If $E^c$ is the complementary event of $E$,then $P(E^c) = 1 - P(E)$
(iii) $0 \leq P(E) \leq 1, \forall E \subseteq S$
(iv) If $E_1 \subseteq E_2$,then $P(E_2) \leq P(E_1)$

Two distinct numbers $a$ and $b$ are chosen randomly from the set $S = \{2^1, 2^2, 2^3, \dots, 2^{25}\}$. What is the probability that $\log_2(ab)$ is an integer?

Four persons $A, B, C$ and $D$ throw an unbiased die, turn by turn in succession till one gets an even number and wins the game. What is the probability that $A$ wins the game if $A$ begins?

There are four machines and it is known that exactly two of them are faulty. They are tested one by one, in a random order until both the faulty machines are identified. The probability that only two tests are needed is:

Four persons $A$, $B$, $C$ and $D$ throw an unbiased die, turn by turn, in succession till one gets an even number and wins the game. What is the probability that $A$ wins if $A$ begins?