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

Given three identical bags each containing $10$ balls,whose colours are as follows:

	Red	Blue	Green
Bag $I$	$3$	$2$	$5$
Bag $II$	$4$	$3$	$3$
Bag $III$	$5$	$1$	$4$

$A$ person chooses a bag at random and takes out a ball. If the ball is Red,the probability that it is from bag $I$ is $p$,and if the ball is Green,the probability that it is from bag $III$ is $q$,then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is:

In an entrance test, there are multiple-choice questions. Each question has four possible answers, only one of which is correct. The probability that a student knows the answer to a question is $90\%$. If the student gets the correct answer to a question, what is the probability that they were guessing?

Bag $A$ contains $2$ white and $3$ red balls. Bag $B$ contains $4$ white and $5$ red balls. One bag is chosen at random and a ball is drawn from it,which is found to be red. Find the probability that it was drawn from bag $B$.

An urn contains $7$ red, $5$ white and $3$ black balls. Three balls are drawn randomly one after the other without replacement. If it is known that the first ball drawn is red and the second ball drawn is white, then the probability that the third ball drawn is not red is

Four boxes $A, B, C$ and $D$ contain $5000, 3000, 2000$ and $1000$ fuses respectively. The percentages of defective fuses in these boxes are $3\%, 2\%, 1\%$ and $0.5\%$ respectively. If a fuse selected at random from one of the boxes is found to be defective, then the probability that it has come from box $D$ is