$A$ and $B$ are two independent events such that $P(A) = \frac{1}{2}$ and $P(B) = \frac{1}{3}$. Then $P$ (neither $A$ nor $B$) is equal to

$A$ pandemic has been spreading all over the world. The probabilities are $0.7$ that there will be a lockdown,$0.8$ that the pandemic is controlled in one month if there is a lockdown,and $0.3$ that it is controlled in one month if there is no lockdown. The probability that the pandemic will be controlled in one month is

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

From a pack of $52$ cards,two cards are drawn one by one without replacement. The probability that the first drawn card is a king and the second is a queen,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.