$A$ 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?

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

Consider the circuit. If the probability that each switch is closed is $p$,then find the probability of current flowing through $AB$.

$A$ 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?

If $A$ and $B$ are independent events and $P(A)=\frac{2}{3}$ and $P(B)=\frac{3}{5}$,then $P(A^{\prime} \cap B)$ is equal to:

An urn contains $10$ black and $5$ white balls. Two balls are drawn from the urn one after the other without replacement. What is the probability that both drawn balls are black?