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

An urn contains $4$ red and $5$ white balls. Two balls are drawn one after the other without replacement,then the probability that both the balls are red is

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

If $A$ and $B$ are two independent events such that $P(A) = 0.40$ and $P(B) = 0.50$,find $P(\text{neither } A \text{ nor } B)$.

$A$ bag contains $4$ red and $3$ black balls. $A$ second bag contains $2$ red and $3$ black balls. One bag is selected at random. If from the selected bag,one ball is drawn at random,then the probability that the ball drawn is red,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?