Basics of Probability

Numbers $1$ to $10$are written on ten separates slips (one number on one slip ), kept in a box, and mixed well. One slip is chosen from the box without looking into it. Answer the following questions.

What is the probability of getting a number greater than $6$?

Numbers $1$ to $10$are written on ten separates slips (one number on one slip ), kept in a box and mixed well. One slip is chosen from the box without looking into it. Answer the following questions.

What is the probability of getting an even number?

Two dice are rolled at a time. What is the probability of getting number $6$ in two dice?

Study the given information and answer the following question --
An urn contains $4$ Green, $3$ Red and $5$ Blue balls.
What is the probability that at least one is Blue, if $4$ balls are picked at random ?

Numbers $1$to $10$are written on ten separates slips (one number on one slip ), kept in a box, and mixed well. One slip is chosen from the box without looking into it .  Answer the following questions.

What is the probability of getting a $1-$digit number ?

Numbers $1 \mathrm{to} 10$ are written on ten separates slips (one number on one slip), kept in a box, and mixed well. One slip is chosen from the box without looking into it. Answer the following questions.

What is the probability of getting a number less than $6$?

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

Two events $A$ and $B$ have probabilities $0.25$ and $0.50$ respectively. The probability that both $A$ and $B$ occur simultaneously is $\mathrm{0.14.}$ Then the probability that neither $A$ nor $B$ occurs 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:

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals

A five digit number is formed by the digits $1, 2, 3, 4, 5$ with no digit being repeated. The probability that the number is divisible by $4$, is

Determine  the chance that a non-leap year selected at random will not contain $53$ Sundays or $53$ Mondays?

If $\Delta ABC$ is a right angle triangle with $\angle ACB$ as its right angle. The measure of $\angle ABC=60°$ and $AB=10.$ Let $P$ be randomly chosen inside $ABC,$ and extend $BP$ to meet $AC$ at $D.$ Then, the probability that $BD>5\sqrt{2}$ is

Let $E$ be an event in sample space and $E^{\text{'}}$ be its complement. If $P\left(E\right)=\frac{1}{4}$. Find $P\left(E\cup E^{\text{'}}\right)$.

Let $E$ be an event in sample space and $E^{\text{'}}$ be its complement. If $P\left(E\right)=\frac{2}{3}$. Find $P\left(E\cup E^{\text{'}}\right)$.

Let $E$ be an event in sample space and $E^{\text{'}}$ be its complement. If $P\left(E\right)=\frac{1}{3}$. Find $P\left(E\cup E^{\text{'}}\right)$.

Let $E$ be an event in sample space and $E^{\text{'}}$ be its complement. If $P\left(E\right)=\frac{1}{2}$. Find $P\left(E\cup E^{\text{'}}\right)$.

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

$A$ and $B$ throws a pair of dice. If $A$ throws $9$ and $B$'s chance of throwing a higher number is $\frac{k}{6}$, then the value of $k$ is _____