A determinant is chosen at random. The set of all determinants of order $2$ with elements $0$ or $1$ only. The probability that value of the determinant chosen is positive, is

Two dice are thrown. The events $A, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

Describe the events not $B$

Two cards are drawn one by one at random from a pack of $52$ cards. The probability that both of them are king, is

Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace

Cards are drawn one by one without replacement from a pack of $52$ cards. The probability that $10$ cards will precede the first ace is

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is