Definition of Probability

Three identical dice are rolled. The probability that the same number will appear on each of them is

If the integers $m \& n$ are chosen at random from $1$ to $100$, then the probability that a number of the form $7^m+7^n$ is divisible by $5$ equals:

In a lottery, containing $35$ tickets, exactly $10$ tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is

A box contains $100$ balls, numbered from $1$ to $100$. If $3$ balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd number, is

Two bolts, two nuts and three needles are in a box. Two parts are chosen at random from the box. What is the probability that one is a bolt and one is a needle?

Let $S$ be the set of all quadratic equations of the form $x^2+bx+c=0$ where $b,c\in$ $\{1,2,3,4,5,6\}$. If an equation is selected at random from $S$, then the probability that the equation has real roots is

Three numbers are chosen at random without replacement from the set $A=\{x\in Z\mid 2\le x\le 11\}.$ The probability that the minimum of choosen numbers is $3$ and maximum is $7$ is

If $p$ and $q$ are chosen at random from the set $\{1,2,3$, $\dots ,10\}$, with replacement, then the probability that the roots of equation $x^2+px+q=0$ are real, is

A box contains $6$ red ball and $2$ black balls. Two balls are drawn at random from it without replacement. If $X$ denotes the number of red balls drawn, then $E\left(X\right)$ is equal to

In a box there are $8$ red, $7$ blue, and $6$ green balls. One ball is picked up randomly. What is the probability that it is neither red nor green?

In three throws of two dice, the probability of throwing doublets not more than twice is :

Seven balls are drawn simultaneously from a bag containing $5$ white and $6$ green balls. The probability of drawing $3$ white and $4$ green balls is

A complete cycle of a traffic light takes $60 \mathrm{s}$. During each cycle the light is green for $25 \mathrm{s}$, yellow for $5 \mathrm{s}$ and red for $30 \mathrm{s}$. At a randomly chosen time, the probability that the light will not be green, is

12 different balls are distributed among 3 distinct boxes. The probability that the $1^{st}$ box contains 3 balls is

A bag contains $5$ white and $7$ black balls and a man draws $4$ balls at random. The odds against these being all black is:

Probability of a $3$ digit number having all the digits same is

In a lottery three were$90$ tickets numbered $1$ to $90$. Five tickets were drawn at random. The probability that two of the tickets drawn numbers $15$ and $89$, is

A box contains $10$ tickets numbered $1,2,...,10$. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than $10$. The probability that the minimum number on them is $5$ is

A dice is rolled three times, then the probability of getting a larger number than the previous number each time is

The probability of forming a three digit numbers with all 3 digits being same when three digit numbers are formed out of the digit 0, 2, 4, 6, 8 is