From a pack of $52$ cards two cards are drawn in succession one by one without replacement. The probability that both are aces is
$\frac{2}{{13}}$
$\frac{1}{{51}}$
$\frac{1}{{221}}$
$\frac{2}{{21}}$
A card is selected from a pack of $52$ cards. How many points are there in the sample space?
If $E$ and $F$ are events with $P\,(E) \le P\,(F)$ and $P\,(E \cap F) > 0,$ then
In a class of $60$ students, $40$ opted for $NCC,\,30$ opted for $NSS$ and $20$ opted for both $NCC$ and $NSS.$ If one of these students is selected at random, then the probability that the student selected has opted neither for $NCC$ nor for $NSS$ is
Let $E _{1}, E _{2}, E _{3}$ be three mutually exclusive events such that $P \left( E _{1}\right)=\frac{2+3 p }{6}, P \left( E _{2}\right)=\frac{2- p }{8}$ and $P \left( E _{3}\right)$ $=\frac{1- p }{2}$. If the maximum and minimum values of $p$ are $p _{1}$ and $p _{2}$, then $\left( p _{1}+ p _{2}\right)$ is equal to.
Choose a number $n$ uniformly at random from the set $\{1,2, \ldots, 100\}$. Choose one of the first seven days of the year $2014$ at random and consider $n$ consecutive days starting from the chosen day. What is the probability that among the chosen $n$ days, the number of Sundays is different from the number of Mondays?