In an entrance test, there are multiple-choice questions. There are four possible answers to each question, of which one is correct. The probability that a student knows the answer to a question is $9/10$. If he gets the correct answer to a question, then the probability that he was guessing 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:

$A$ car manufacturing factory has two plants $X$ and $Y$. Plant $X$ manufactures $70 \%$ of cars and plant $Y$ manufactures $30 \%$ of cars. $80 \%$ of cars at plant $X$ and $90 \%$ of cars at plant $Y$ are rated as standard quality. $A$ car is chosen at random and is found to be standard quality. The probability that it has come from plant $X$ is

Bag $I$ contains $3$ red,$4$ black,and $3$ white balls. Bag $II$ contains $2$ red,$5$ black,and $2$ white balls. One ball is transferred from Bag $I$ to Bag $II$,and then a ball is drawn from Bag $II$. The ball drawn is found to be black. What is the probability that the transferred ball was red?

In a school there are $3$ sections $A, B$ and $C$. Section $A$ contains $20$ girls and $30$ boys,section $B$ contains $40$ girls and $20$ boys and section $C$ contains $10$ girls and $30$ boys. The probabilities of selecting the section $A, B$ and $C$ are $0.2, 0.3$ and $0.5$ respectively. If a student selected at random from the school is a girl,then the probability that she belongs to section $A$ is

Urn $A$ contains $6$ red and $4$ black balls and urn $B$ contains $4$ red and $6$ black balls. One ball is drawn at random from urn $A$ and placed in urn $B$. Then one ball is drawn at random from urn $B$ and placed in urn $A$. If one ball is now drawn at random from urn $A$,the probability that it is found to be red,is