The following table represents the probability distribution of a random variable $X$ for some $k \in Q$. Find the value of $k$.

$X=x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X=x)$	$0.1$	$k$	$0.2$	$2k$	$0.3$	$k$

In a box,there are $20$ cards,out of which $10$ are labelled as $A$ and the remaining $10$ are labelled as $B$. Cards are drawn at random,one after the other and with replacement,until a second $A$-card is obtained. The probability that the second $A$-card appears before the third $B$-card is

$A$ boy tosses a fair coin $3$ times. If he gets $₹ 2x$ for $x$ heads,then his expected gain equals to $₹........$

$A$ coin is biased so that the head is $3$ times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin,then the mean of $X$ is

Four defective oranges are accidentally mixed with sixteen good ones. Three oranges are drawn from the mixed lot. The probability distribution of defective oranges is

If $P(X=x)=c\left(\frac{2}{3}\right)^x$ for $x=1, 2, 3, 4, \ldots$ is a probability distribution function of a random variable $X$, then the value of $c$ is