Types of Events

A problem in calculus is given to two students $A$ and $B$, whose chances of solving it are $\frac{1}{3}$ and $\frac{1}{4}$ respectively. If the probability of the problem being solved, if both of them try independently is $\frac{m}{n},$ then $m+n=$

An electronic assembly consists of two sub system, say, $A$ and $B$. When $P$($A$ fails) $= 0.2$, $P$($B$ fails alone) $=0.15$, $P$($A$ and $B$ fail) $=0.15$. Evaluate $P(A \mathrm{fails} \mathrm{alone})$.

For next three question please follow the same

$A$ is a set containing $10$ elements. A subset $P$ of $A$ is chosen at random and the set $A$ is reconstructed by replacing the elements of $P$.Another subset $Q$ of $A$ is now chosen at random. Then the probability that if :

$\text{P}\cup \text{Q}=\text{A}$ is

Three coins are tossed once. Let $A$ denote the event ‘three heads show”, $B$ denote the event “two heads and one tail show”, $C$ denote the event” three tails show and $D$ denote the event ‘a head shows on the first coin”. Which events are simple?

Two die are thrown simultaneously. The probability of obtaining a total score of $5$ is

If $A, B \& C$  are mutually exclusive and exhaustive events of a random experiment such that $P\left(B\right)=\frac{3}{2}P\left(A\right)$ and $P\left(C\right)=\frac{1}{2}P\left(B\right),$ then $P\left(A\cup C\right)$ equals to

$A$ and $B$ are to throw $2$ dice. If $A$ throws a sum of $9$ points, then $B^{\text{'}}s$ chance of throwing a higher sum is

Let F denote the set of all onto functions from $A=\left\{a_1 , a_2 , a_3 , a_4\right\} to B=\left\{x,y,z\right\}.$ A function f is chosen at random from F. The probability that $f^{-1}\left(x\right)$ consists of exactly two elements is

In a college of $300$ students, every student reads $5$ newspapers and every newspaper is read by $60$ students. The number of newspapers is

For $n$ independent events $i=1, 2,...,n$. All events are equally likely to occur. The probability that one of the events occurs is

Three coins are tossed together, then the probability of getting at least one head is

The probability that a number $n$ chosen at random from $1 \text{to} 30$, to satisfy  $(n+50/ n)>27$ is