The probability distribution of a discrete random variable X is given as :

x	0	1	2	3	4
P(X=x)	0.1	k	2k	2k	k

The value of K is:

Probability of solving a specific problem independently by A and B are $\frac{1}{2}$ and $\frac{1}{3}$ respectively, then which of the following are True?

[where P(X) denotes the probability of an event X]

(A) P(Problem is solved) = $\frac{2}{3}$

(B) P(Exactly one of them solves the problem) = $\frac{1}{2}$

(C) P(Both of them solve the problem) = $\frac{5}{6}$

(D) P(Atmost one solves the problem) = $\frac{5}{6}$

Choose the correct answer from the options given below:

Two numbers are selected at random (without replacement) from the first three positive integers. Let $X$ denotes the larger of the two integers, then the probability distribution of $X$ is

A and B throw a die alternatively till one of them gets a number more than 4 and wins the game. Then the probability of winning the game by B, if A starts first :

There are two bags. Bag-1 contains $4$ white and $6$ black balls and Bag-2 contains $5$ white and $5$ black balls. A die is rolled, if it shows a number divisible by 3, a ball is drawn from Bag-1, else a ball is drawn from Bag-2. If the ball drawn is not black in colour, the probability that it was not drawn from Bag-2 is :

A and B throw a die alternatively till one of them gets 3 or 6 and wins the game. If B starts the game, then the probability of winning the game by A is

The probability of a shooter of hitting the target is $\frac{1}{4}$. The minimum number of fire needed so that the probability of hitting the target atleast once is greater than $\frac{7}{16}$ is: