$A$ dice is thrown twice. The probability of getting $4, 5$ or $6$ in the first throw and $1, 2, 3$ or $4$ in the second throw is

Boxes $B_1, B_2$,and $B_3$ contain balls as given below:

Box	White	Black
$B_1$	$1$	$2$
$B_2$	$3$	$1$
$B_3$	$2$	$3$

One ball is drawn at random from each box. Then,among the balls drawn,the probability that two are black and one is white,is

$A$ number $n$ is chosen at random from the natural numbers $2$ to $1001$. The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ is:

Let $S$ be the sample space of the random experiment of throwing simultaneously two unbiased dice and $E_k = \{(a, b) \in S : ab = k\}$. If $p_k = P(E_k)$, then which of the following is correct?

The probability of an impossible event,i.e.,$P(\phi)$,is

$A$ die marked $1, 2, 3$ in red and $4, 5, 6$ in green is tossed. Let $A$ be the event 'the number is even' and $B$ be the event 'the number is red'. Are $A$ and $B$ independent?