$A$ three-digit number is formed by using the digits $1, 2, 3,$ and $4$. The probability that the number is divisible by $3$ is:

There are $5$ volumes of Mathematics among $25$ books. They are arranged on a shelf in random order. The probability that the volumes of Mathematics stand in increasing order from left to right (the volumes are not necessarily kept side by side) is

For the two events $A$ and $B$,$P(A) = 0.38$ and $P(B) = 0.41$. What is the value of $P(\text{not } A)$?

$A$ bag $x$ contains $3$ white balls and $2$ black balls and another bag $y$ contains $2$ white balls and $4$ black balls. $A$ bag and a ball out of it are picked at random. The probability that the ball is white,is

$A$ binary number is made up of $16$ bits. The probability of an incorrect bit appearing is $p$ and the errors in different bits are independent of one another. The probability of forming an incorrect number is

$A$ coin is tossed three times in succession. If $E$ is the event that there are at least two heads and $F$ is the event in which the first throw is a head,then $P\left( \frac{E}{F} \right) = $