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 $/ 11$)

$A$ bag contains $6$ balls. If three balls are drawn at a time and all of them are found to be green,then the probability that exactly $5$ of the balls in the bag are green is:

Events $E_{1}$ and $E_{2}$ form a partition of the sample space $S$. $A$ is any event such that $P(E_{1}) = P(E_{2}) = \frac{1}{2}$,$P(E_{2} | A) = \frac{1}{2}$,and $P(A | E_{2}) = \frac{2}{3}$. Then $P(E_{1} | A)$ is:

Box $I$ contains $30$ cards numbered $1$ to $30$ and Box $II$ contains $20$ cards numbered $31$ to $50$. $A$ box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box $I$ is

Two coins $A$ and $B$ are kept in an urn. When coin $A$ is flipped,the probability of getting a head is $1/4$,while for coin $B$ it is $3/4$. One coin is randomly chosen from this bag,tossed twice,and it falls heads on both occasions. The probability that it is coin $A$ is:

Bag $B_1$ contains $6$ white and $4$ blue balls,Bag $B_2$ contains $4$ white and $6$ blue balls,and Bag $B_3$ contains $5$ white and $5$ blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white,then the probability that the ball is drawn from Bag $B_2$ is: