Bag $A$ contains 2 white and 3 red balls and bag $B$ contains 4 white and 5 red balls. If one ball is drawn at random from one of the bags and is found to be red, then the probability that it was drawn from the bag $B$ is

If the probability distribution of a random variable $X$ is as follows, then $k$ is equal to

$$ \begin{array}{c|l|l|l|l} \hline X=x & 1 & 2 & 3 & 4 \\ \hline P(X=x) & 2 k & 4 k & 3 k & k \\ \hline \end{array} $$

In a binomial distribution $B(n, p)$ the sum and product of the mean and the variance are 5 and 6 respectively, then $6(n+p-q)$ is equal to

If each of the coefficients $a, b$ and $c$ in the equation $a x^2+b x+c=0$ is determined by throwing a die, then the probability that the equation will have equal roots, is