$A$ 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

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:

Two groups are competing for the position on the board of directors of a corporation. The probabilities that the first and the second groups will win are $0.6$ and $0.4$ respectively. Further,if the first group wins,the probability of introducing a new product is $0.7$ and the corresponding probability is $0.3$ if the second group wins. Find the probability that the new product was introduced by the second group. (in $/9$)

$A$ 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

An unbiased coin is tossed. If the outcome is a head,then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in a tail,then a card from a well-shuffled pack of nine cards numbered $1, 2, 3, \dots, 9$ is randomly picked and the number on the card is noted. The probability that the noted number is either $7$ or $8$ is

Meera visits only one of the two temples $A$ and $B$ in her locality. The probability that she visits temple $A$ is $\frac{2}{5}$. If she visits temple $A$,the probability that she meets her friend is $\frac{1}{3}$,whereas it is $\frac{2}{7}$ if she visits temple $B$. Meera met her friend at one of the two temples. The probability that she met her at temple $B$ is