Embibe Experts Solutions for Exercise 4: Assignment

Out of $20$ consecutive numbers, two are chosen at random, the probability that their sum is odd is

$A$ and $B$ play with two dice on the condition that $A$ wins if he throws $6$ before $B$ throws $7$, then the probability that $A$ wins is if $A$ start throwing

Two distinct numbers are selected at random from the first twenty natural numbers. The probability that the sum will be divisible by $3$ is $\frac{p}{q}$, where $p,q$ are coprime then $\left(p+q\right)$ is equal to

Three numbers $a,b$ and $c$ are selected from the set $\left\{1,3,5,7,9,11,13\right\}$ then the probability that $a+b+c=13$ is$\frac{p}{q}$, where $p$ and $q$ are coprime then $p+q$ is equal to

Out of all possible numbers formed by using all the digits $1,2,3,4,3,2,1$.  A number is selected then the probability that selected number has its odd digits at odd places is $\frac{1}{N}$, then $N$ is equal to

Out of all positive integral divisors of $240$ one of them is selected then the probability that it is in the form $4n+2,\left(n\ge 0\right)$ is $\frac{1}{N}$ then $N$ is

If four squares are chosen at random on a chess board. If the probability that they lie on a diagonal line is $P$ then $158844 P$ is

$A, B$ and $C$, play a game and chances of their winning it in an attempt are $\frac{2}{3},\frac{1}{2}$ and $\frac{1}{4}$, respectively. $A$, has the first chance followed by $B$, and then by $C$. This is repeated till one of them wins the game. Let $x,y,z$, are their respective chances of winning the game, then $\frac{x}{z}$, is