$A$ certain disease has a prevalence of $1\%$ in the population. $A$ diagnostic test for the disease has a sensitivity of $98\%$ and a specificity of $95\%$. If a person from this population tests positive, then the probability that they actually have the disease is... (in $\%$)

$A$ bag contains $8$ balls,whose colors are either white or black. $4$ balls are drawn at random without replacement and it was found that $2$ balls are white and $2$ balls are black. The probability that the bag originally contained an equal number of white and black balls is:

Three similar urns $A, B, C$ contain $2$ red and $3$ white balls; $3$ red and $2$ white balls; $1$ red and $4$ white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from urn $C$ is

$A$ manufacturing company of bulbs has $3$ units $A, B$ and $C$ which produce $25 \%$,$35 \%$ and $40 \%$ of the bulbs respectively. Out of the bulbs produced by $A, B, C$ units,$5 \%, 4 \%$ and $2 \%$ are defective respectively. If a bulb is chosen at random and found to be defective,then the probability that it is produced by unit $B$ is

Three urns $A$,$B$,and $C$ contain $7$ red,$5$ black; $5$ red,$7$ black; and $6$ red,$6$ black balls,respectively. One of the urns is selected at random and a ball is drawn from it. If the ball drawn is black,then the probability that it is drawn from urn $A$ is:

The probabilities of having a defective toy in three cartons $A, B, C$ are $\frac{1}{3}, \frac{1}{4}, \frac{2}{5}$ respectively. If a carton is selected at random and a toy drawn randomly from it is found to be defective,then the probability that it is drawn from carton $B$ is