$A$ letter is known to have come either from $LONDON$ or $CLIFTON$; on the postmark only the two consecutive letters $ON$ are legible. The probability that it came from $LONDON$ is

$A$ shopkeeper buys a particular type of electric bulbs from three manufacturers $M_1, M_2$,and $M_3$. He buys $25 \%$ of his requirement from $M_1$,$45 \%$ from $M_2$,and $30 \%$ from $M_3$. Based on past experience,he found that $2 \%$ of type $M_3$ bulbs are defective,whereas only $1 \%$ of type $M_1$ and type $M_2$ bulbs are defective. If a bulb chosen by him at random is defective,then the probability that it was of type $M_3$ is

The probability that a person goes to college by car is $\frac{1}{5}$,by bus is $\frac{2}{5}$,and by train is $\frac{3}{5}$. The probabilities that he reaches the college late if he takes a car,bus,or train are $\frac{2}{7}$,$\frac{4}{7}$,and $\frac{1}{7}$ respectively. If he reaches the college in time,the probability that he traveled by car 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:

$A$ box $B_1$ contains $3$ blue balls and $6$ red balls. Another box $B_2$ contains $8$ blue balls and $n$ red balls $(n \in N)$. $A$ ball selected at random from a box is found to be red. If $p$ is the probability that this red ball drawn is from box $B_2$,then

$A$ bag contains $10$ balls out of which $k$ are red and $(10-k)$ are black,where $0 \le k \le 10$. If three balls are drawn at random without replacement and all of them are found to be black,then the probability that the bag contains $1$ red and $9$ black balls is: