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 :

The random variable X has a probability distribution P(X) of the following form, where k is some number.

$P(X=x) = \begin{cases} k, & \text{if } x=0 \\ 2k, & \text{if } x=1 \\ 3k, & \text{if } x=2 \\ 0, & \text{otherwise} \end{cases}$

Then $P(x \leq 2)$ is :

The probability that he copied it given that his answer is correct :

If E and F are two events such that $P(E \cup F)=P(E)$, then

Two numbers are selected at random from the integers 1 through 19. If the sum is even, then the probability that both are odd numbers is:

The probability of answering a question correctly, is :

If the probability distribution of a random variable X is as given below :

Then the value of K is :