$A$ bag contains $10$ white and $15$ red balls. If two balls are drawn one after another,what is the probability that the first ball is red and the second ball is white?

Two urns identical in appearance contain respectively $3$ green and $2$ black balls and $2$ green and $5$ black balls. One urn is selected at random and a ball is drawn from it. The probability that it is black is

Bag $A$ contains $4$ white and $2$ black balls, bag $B$ contains $3$ white and $3$ black balls, and bag $C$ contains $2$ white and $4$ black balls. If a bag is chosen at random and a ball is chosen at random from it, then the probability that the ball drawn is black is

If two cards are drawn one after the other without replacement from a well-shuffled ordinary deck of $52$ cards, then the probability that both of them are aces is

$A$ woman has $10$ keys,out of which only one opens a lock. She tries the keys one after another (keeping aside the failed ones) until she succeeds in opening the lock. What is the probability that the seventh key works?

Two balls are drawn at random with replacement from a box containing $10$ black and $8$ red balls. Find the probability that the first ball is black and the second is red.