Basic Terminologies in Probability

One box contains four cards numbered $1, 3, 5$ and $6$. Another box contains three cards numbered $2, 4$ and $7$. One card is drawn from each box. Find the probability that the sum is even.

The face of a coin is either head or tail. If three coins are tossed, what is the probability of getting three tails or three heads?

Two fair dice are thrown. What is the probability that the sum of the dice is divisible by 5?

Two people are chosen randomly from four married couples. What is the probability that they are husband and wife?

A two-digit number is chosen randomly. What is the probability that it is divisible by $7$?

If two balls are drawn in succession from five white and four yellow, find the probability that all are of one colour if the first ball is replaced immediately before the second draw.

In a dice game, one fair is used. The player wins if he rolls either $1$ or $6$. He losses if he turns up any other face. What is the expected winning for one roll of the die?

An urn contains four black balls and six white balls. What is the probability of getting one black ball and white ball in two consecutive draws from the urn?

One letter is taken from each of the words PARALLEL and LEVEL at random. What is the probability of getting the same letter?

The probability of getting credit in an examination is $\frac{1}{3}$. If three students are selected at random, what is the probability that at least one of them got a credit?

A standard deck of $52$ playing cards is well shuffled. What is the approximate probability that the first four cards dealt from the deck will be four aces?

A face of a coin is either head or tail. If three coins are tossed, what is the probability of getting three tails?

Consider an experiment of tossing a coin repeatedly until the outcomes of two consecutive tosses are same. If the probability of a random toss resulting in head is $\frac{1}{3}$, then the probability that the experiment stops with head is

Let $X=\left\{\left(x, y\right)\in \mathrm{\mathbb{Z}}\times \mathrm{\mathbb{Z}} : \frac{x^2}{8}+\frac{y^2}{20}<1 \mathrm{and} y^2<5\mathrm{x}\right\}$. Three distinct point $P, Q$ and $R$ are randomly chosen from $X$. Then the probability that $P, Q$ and $R$ form a triangle whose area is a positive integer, is

Three dice are thrown. What is the probability that each face shows only multiples of $3$?

One bag contains $3$ white and $2$ black balls, another bag contains $2$ white and $3$ black balls. Two balls are drawn from the first bag and put it into the second bag and then a ball is drawn from the second bag. What is the probability that it is white?

$A$ and $B$ play a game where each is asked to select a number from $1 \text{to} 25$.If the numbers selected by $A$ and $B$ match, both of them win a prize. The probability that they win their prize on $5^{th}$ game is equal to 

In a family there are $3$ children. The probability that the family has no male child assuming that the chance of a child being a male or female are equal is

When two dice are thrown, the probability of getting a prime number on one die and a composite number on the other is

If $x$ is chosen at random from the set $\left\{1,2.3,4\right\}$ and $y$ is chosen at random from the set $\left\{5,6,7\right\}$, then the probability that xy will be even is