If $f(x) = \begin{cases} 3(1 - 2x^2) & ; 0 < x < 1 \\ 0 & ; \text{otherwise} \end{cases}$ is a probability density function of $X$,then $P\left(\frac{1}{4} < x < \frac{1}{3}\right)$ is

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

The following is the probability distribution of $X$:

$X$	$0$	$1$	$2$	$3$
$P(X=x)$	$\frac{1+p}{5}$	$\frac{2-2p}{5}$	$\frac{2-p}{5}$	$\frac{2p}{5}$

For a minimum value of $p$,the value of $5 E(X)$ is:

Find the probability distribution of the number of tails in the simultaneous tosses of three coins.

$A$ random variable $X$ has the following probability distribution:

$X = x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X = x)$	$0$	$k$	$2k$	$2k$	$3k$	$k^2$	$2k^2$	$7k^2 + k$

Then $F(4) = $

$A$ random variable $X$ has the following probability distribution:
| $x$ | $1$ | $2$ | $3$ | $4$ | $5$ | $6$ | $7$ | $8$ |
|---|---|---|---|---|---|---|---|---|
| $P(x)$ | $0.15$ | $0.23$ | $0.12$ | $0.10$ | $0.20$ | $0.08$ | $0.07$ | $0.05$ |
For the events $E = \{x \text{ is a prime number}\}$ and $F = \{x < 4\}$,the probability $P(E \cup F)$ is: