Two events $A$ and $B$ will be independent,if

If $A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{5}$,then which of the following is true?

The probability that the product of the outcomes when three dice are rolled simultaneously is divisible by $4$ is equal to

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:

Let a computer program generate only the digits $0$ and $1$ to form a string of binary numbers. The probability of occurrence of $0$ at even places is $\frac{1}{2}$ and the probability of occurrence of $0$ at odd places is $\frac{1}{3}$. Then the probability that $'10'$ is followed by $'01'$ is equal to:

Two players $A$ and $B$ alternatively toss $3$ coins simultaneously. The player who gets $2$ heads and $1$ tail first, wins the game. If the game continues until someone wins and if $A$ begins the game, the probability that $B$ wins the game is