Axiomatic Approach to Probability

If a coin is tossed thrice, find the probability of getting one or two heads.

From a lot of $\mathrm{}30\mathrm{}$ bulbs which include $\mathrm{}6\mathrm{}$ defectives, a sample of $\mathrm{}4\mathrm{}$ bulbs are drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

If a teacher has a question bank consisting of $300$ easy T/F questions, $200$ difficult T/F questions, $500$ easy MCQ and $600$ difficult MCQ, then a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a MCQ is:

A point $\left(\alpha , \beta \right), \alpha , \beta \in I$ is selected at random from inside the triangle formed by $x+y=10$ and both co-ordinate axes. If $\alpha , \beta$ are odd integers, then probability that both $\alpha , \beta$ are prime numbers is

If we divide 3888 by a two digit integer, the resultant is an integer. What is the probability that the resultant is a three digit integer?

Three natural numbers are taken at random one by one with replacement from the set

$A=\left\{x|1\le x\le 100,x\in N\right\}.$ The probability that the $AM$ of the number is $25$ is

Study the given information carefully to answer the questions that follow.

A box contains 4 green, 5 blue, 2 red and 3 yellow marbles.
If three marbles are drawn at random, what is the probability that none is green?

Consider a set 'P' containing 'n' elements. A subset 'A' of 'P' is drawn and there after set 'P' is reconstructed. Now one more subset 'B' of 'P' is drawn. Probability of drawing sets A and B so that $A\cap B$ has exactly one element -

Let $20$ distinct balls have been randomly distributed in to $4$ distinct boxes, $5$ into each. Let '$A$' be the event that two specific balls have been put into a particular box. The probability of occurrence of event '$A$' is :

A box contains tickets numbered $1$ to $N. n$ tickets are drawn from the box with replacement. The probability that the largest number on the tickets is $k$ is

Three boxes are labelled A, B and C and each box contains four balls numbered 1, 2, 3 and 4. The balls in each box are well mixed. A child choose one ball at random from each of the three boxes. If a, b and c are the numbers on the balls chosen from the boxes A, B and C respectively, the child wins a toy helicopter when a = b + c. The odds in favour of the child to receive the toy helicopter are -

Let the 9 different letters A, B, C, .... I $ϵ$ {1, 2, 3, .... 9} then the probability that product $\left(A-1\right)\left(B-1\right)\dots ..\left(I-9\right)$ is even number will be -

A box contains cards numbered from 2 to 101. What is the probability that a picked up card is a perfect square.

Two dice are thrown simultaneously. The probability that sum is odd or less than $7$ or both, is

For any two events $A$ & $B$

Three numbers are chosen at random without replacement from the set $A=\left\{x|1\le x\le 10, x\in N\right\}.$ The probability that the minimum of the chosen numbers is $3$ and maximum is $7$, is

From a group of 10 persons consisting of 5 lawyers, 3 doctors and 2 engineers, four persons are selected at random. The probability that the selection contains at least one of each category is-

4 gentlemen and 4 ladies take seats at random round a table. The probability that they are sitting alternately is-

If the letters of the word ATTEMPT are written down at random, the chance that all Ts are consecutive is-

The probability of having at least one tail in $4$ throws with a coin is-