Bag $1$ contains $4$ white balls and $5$ black balls,and Bag $2$ contains $n$ white balls and $3$ black balls. One ball is drawn randomly from Bag $1$ and transferred to Bag $2$. $A$ ball is then drawn randomly from Bag $2$. If the probability that the ball drawn from Bag $2$ is white is $29/45$,then $n$ is equal to:

Suppose that a bag $A$ contains $n$ red and $2$ black balls and another bag $B$ contains $2$ red and $n$ black balls. One of the two bags is selected at random and two balls are drawn from it at a time. When it is known that the two balls drawn are red,if the probability that those two balls drawn are from bag $A$ is $\frac{6}{7}$,then $n=$

$A$ card from a pack of $52$ cards is lost. From the remaining cards of the pack,two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.

$A$ manufacturer has three machine operators $A$,$B$,and $C$. The first operator $A$ produces $1 \%$ defective items,whereas the other two operators $B$ and $C$ produce $5 \%$ and $7 \%$ defective items respectively. $A$ is on the job for $50 \%$ of the time,$B$ is on the job for $30 \%$ of the time,and $C$ is on the job for $20 \%$ of the time. If a defective item is produced,what is the probability that it was produced by $A$ (in $/34$)?

$A, B_1, B_2, B_3$ are the events in a random experiment. If $P(B_1)=0.25, P(B_2)=0.30, P(B_3)=0.45, P(A|B_1)=0.05, P(A|B_2)=0.04, P(A|B_3)=0.03$, then $P(B_2|A) = $

$A$ bag contains $4$ red and $4$ black balls,another bag contains $2$ red and $6$ black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.