$A$ bag contains $4$ red and $3$ blue balls. Two balls are drawn one after another. If the first ball is replaced before drawing the second,what is the probability that the first ball is red and the second ball is blue?

$A$ purse contains $4$ copper coins and $3$ silver coins. $A$ second purse contains $6$ copper coins and $4$ silver coins. $A$ purse is chosen randomly and a coin is taken out of it. What is the probability that it is a copper coin?

If $A_i$ $(i=1, 2, 3, \ldots, n)$ are $n$ independent events with $P(A_i) = \frac{1}{1+i}$ for each $i$,then the probability that none of $A_i$ occurs 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

Let $A$ and $B$ be independent events with $P(A)=0.3$ and $P(B)=0.4$. Find $P(A \cap B)$.

$A$ 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?