Three similar urns $A, B, C$ contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from urn $C$ is

If a random variable X has the following probability distribution, then the mean of $X$ is $$ \begin{array}{c|c|c|c|c} X=x_1 & 1 & 2 & 3 & 5 \\ \hline p\left(X=x_i\right) & 2 k^2 & k & k & k^2 \end{array} $$

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is

When 2 dice are thrown, it is observed that the sum of the numbers appeared on the top faces of both the dice is a prime number. Then, the probability of having a multiple of 3 among the pair of numbers thus obtained is