For the two events $A$ and $B$, $P(A) = 0.38,\,$ $P(B) = 0.41,$ then the value of $P(A$ not) is

A bag contains $3$ red and $7$ black balls, two balls are taken out at random, without replacement. If the first ball taken out is red, then what is the probability that the second taken out ball is also red

Two dice are thrown and the sum of the numbers which come up on the dice is noted. Let us consider the following events associated with this experiment

$A:$ $^{\prime}$ the sum is even $^{\prime}$.
$B:$ $^{\prime}$the sum is a multiple of $3$$^{\prime}$
$C:$ $^{\prime}$the sum is less than $4 $$^{\prime}$
$D:$ $^{\prime}$the sum is greater than $11$$^{\prime}$.

Which pairs of these events are mutually exclusive ?

From $10,000$ lottery tickets numbered from $1$ to $10,000$, one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by $20$

On her vacations Veena visits four cities $(A,\,B ,\, C$ and $D$ ) in a random order. What is the probability that she visits $A$ first and $B$ last ?

Two dice are thrown simultaneously. What is the probability of obtaining a multiple of $2$ on one of them and a multiple of $3$ on the other