An examination is attempted by $5000$ graduates, $2000$ post-graduates, and $1000$ doctorate holders. The probabilities that a graduate, a post-graduate, and a doctorate holder will pass the examination are $\frac{2}{3}$, $\frac{3}{4}$, and $\frac{4}{5}$ respectively. If one of the examinees passed the examination, then the probability that he is a post-graduate is:

Three boxes $B_1$,$B_2$ and $B_3$ contain balls with different colors as follows:

Box	White,Black,Red
$B_1$	$2, 1, 2$
$B_2$	$3, 2, 4$
$B_3$	$4, 3, 2$

$A$ die is thrown. Box $B_1$ is chosen if either $1$ or $2$ turns up. Box $B_2$ is chosen if $3$ or $4$ turns up and box $B_3$ is chosen if $5$ or $6$ turns up. Having chosen a box in this way,a ball is drawn at random from that box. If the ball drawn is found to be Red,then the probability that it is drawn from box $B_2$ is

In a certain college, $4 \%$ of men and $1 \%$ of women are taller than $1.8 \ m$. Also, $60 \%$ of students are women. If a student selected at random is found to be taller than $1.8 \ m$, then the probability that the student is a woman is: (in $/ 11$)

$70 \%$ of the total employees of a factory are men. Among the employees of that factory,$30 \%$ of men and $15 \%$ of women are technical assistants. If an employee chosen at random is found to be a technical assistant,then the probability that this employee is a man is

$A$ bag contains $5$ balls of unknown colours. There are equal chances that out of these five balls,there may be $0, 1, 2, 3, 4,$ or $5$ red balls. $A$ ball is taken out from the bag at random and is found to be red. The probability that it is the only red ball in the bag is

In an examination, there are $4$ Yes/No type questions. The probability that a student answers a question correctly without guessing is $2/3$. The probability that a student guesses a correct answer is $1/2$. $A$ student writes the examination either by not guessing any of the $4$ questions or by guessing all $4$ questions. The probability that they attempt the exam by guessing all questions is $3/7$. Given that a student answered at least $3$ questions correctly, what is the probability that they answered all questions without guessing?