If two dice are thrown simultaneously,then the probability that $1$ comes on the first die is:

One ticket is selected at random from $100$ tickets numbered $00, 01, 02, \dots, 98, 99$. If $X$ and $Y$ denote the sum and the product of the digits on the tickets respectively,then $P(X = 9 | Y = 0)$ equals:

The probability of getting head and tail alternately in three throws of a coin (or a throw of three coins) is:

What is the probability that a leap year selected at random will contain $53$ Sundays?

$A$ locker can be opened by dialing a fixed three-digit code (between $000$ and $999$). $A$ stranger who does not know the code tries to open the locker by dialing three digits at random. The probability that the stranger succeeds at the $k^{th}$ trial is

Two integers are chosen at random and multiplied. The probability that the product is an even integer is