In four schools $B_1, B_2, B_3, B_4$,the percentage of girl students is $12, 20, 13, 17$ respectively. From a school selected at random,one student is picked up at random and it is found that the student is a girl. The probability that the school selected is $B_2$ is:

$A$ pack of playing cards was found to contain only $51$ cards. If the first $13$ cards which are examined are all red,then the probability that the missing card is black,is

There are three families $F_1, F_2, F_3$. $F_1$ has $2$ boys and $1$ girl; $F_2$ has $1$ boy and $2$ girls; $F_3$ has $1$ boy and $1$ girl. $A$ family is randomly chosen and a child is chosen from that family randomly. If it is known that the child thus selected is a girl,then the probability that she is from $F_2$ is

For $k=1, 2, 3$,the box $B_k$ contains $k$ red balls and $(k+1)$ white balls. Let $P(B_1) = \frac{1}{2}$,$P(B_2) = \frac{1}{3}$,and $P(B_3) = \frac{1}{6}$. $A$ box is selected at random and a ball is drawn from it. If a red ball is drawn,then the probability that it comes from box $B_2$ is:

In a bolt factory,machines $A, B$ and $C$ manufacture respectively $20 \%$,$30 \%$ and $50 \%$ of the total bolts. Of their output,$3 \%$,$4 \%$ and $2 \%$ are respectively defective bolts. $A$ bolt is drawn at random from the product. If the bolt drawn is found to be defective,then the probability that it is manufactured by the machine $C$ is

Bag $I$ contains $3$ red and $4$ black balls. Bag $II$ contains $5$ red and $6$ black balls. If one ball is drawn at random from one of the bags, and it is found to be red, then the probability that it was drawn from Bag $II$, is