$A$ bag contains $6$ balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least $5$ black balls is

$A$ bag $A$ contains $2$ white and $3$ red balls and bag $B$ contains $4$ white and $5$ red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag $B$ 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

There are three bags $X$,$Y$,and $Z$. Bag $X$ contains $5$ one-rupee coins and $4$ five-rupee coins; Bag $Y$ contains $4$ one-rupee coins and $5$ five-rupee coins; and Bag $Z$ contains $3$ one-rupee coins and $6$ five-rupee coins. $A$ bag is selected at random and a coin drawn from it at random is found to be a one-rupee coin. Then the probability that it came from bag $Y$ is:

Four boxes $A, B, C$ and $D$ contain $5000, 3000, 2000$ and $1000$ fuses respectively. The percentages of defective fuses in these boxes are $3\%, 2\%, 1\%$ and $0.5\%$ respectively. If a fuse selected at random from one of the boxes is found to be defective, then the probability that it has come from box $D$ is

Suppose we have four boxes $A, B, C$ and $D$ containing coloured marbles as given below:

Box	Red	White	Black
$A$	$1$	$6$	$3$
$B$	$6$	$2$	$2$
$C$	$8$	$1$	$1$
$D$	$0$	$6$	$4$

One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red,what is the probability that it was drawn from box $A$,box $B$,or box $C$?