The probability distribution of a random variable $X$ is given below.

$X = x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(x)$	$0.01$	$0.10$	$0.26$	$0.33$	$0.18$	$0.06$	$K$	$0.04$

Then $P(X \geq 3) - P(X < 6) =$

Face masks are supplied to a junior college in packets of $100$. If there is a chance that $1$ in $500$ face masks is defective, then the number of packets containing no defective face masks in a consignment of $10,000$ packets is:

If the probability distribution of a random variable $X$ is as follows, then the variance of $X$ is
$\begin{array}{|c|c|c|c|c|}\hline X=x & 2 & 3 & 5 & 9 \\\hline P(X=x) & K & 2 K & 3 K^2 & K^2 \\\hline\end{array}$

$A$ person plays a game of tossing a coin thrice. For each head,he is given $Rs. 2$ by the organiser of the game and for each tail,he has to give $Rs. 1.50$ to the organiser. Let $X$ denote the amount gained or lost by the person. Show that $X$ is a random variable and exhibit it as a function on the sample space of the experiment.

An unbiased coin is tossed $5$ times. Suppose that a variable $X$ is assigned the value $k$ when $k$ consecutive heads are obtained for $k=3, 4, 5$; otherwise,$X$ takes the value $-1$. Then the expected value of $X$ is:

$A$ coin is tossed three times. If $X$ denotes the absolute difference between the number of heads and the number of tails,then $P(X=1) = $