The feasible region represented by the constraints $y - 2x \leq 4, x + y \geq 5, x \leq 4, y \geq 2, x, y \geq 0$ is ...........

A fair die is thrown at random. Let A be the event that the number obtained on the die is a non-even prime number and B be the event that the number obtained on the die is an odd number.
Let $p : P(A) = \dfrac{1}{3}$, $q$ : A and B are independent events.
Then the truth values of statements $p$ and $q$ respectively are.....

Three ships A, B, C sail from England to India. If the odds in favour of their safe arrival are 2:5, 3:7 and 6:11 respectively, then the probability that the exactly two ships arrive safely is

A random variable X has the probability distribution

$X = x$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X = x)$	$0.23$	$0.15$	$0.12$	$0.10$	$0.20$	$0.07$	$0.08$	$0.05$

for the events E = {X is a prime number} and F = {X $\leq$ 3}, then P (E$\cup$F)=