A coin is tossed once. Write its sample space.

If a coin is tossed two times, describe the sample space associated to this experiment.

If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this experiment.

Write the sample space for the experiment of tossing a coin four times.

Two dice are thrown. Describe the sample space of this experiment.

What is the total number of elementary events associated to the random experiment of throwing three dice together?

A coin is tossed and then a die is thrown. Describe the sample space for this experiment.

A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.

A coin is tossed twice. If the second throw results I a tail, a die is thrown. Describe the sample space for this experiment.

An experiment consists of tossing a coin and then tossing it second time if head occurs. If a tail occurs on the first toss, then a die is tossed once. Find the sample space.

A coin is tossed. If it shows tail, we draw a ball from a box which contains 2 red 3 black balls; it shows head, we throw a die. Find the sample space of this experiment.

A coin is tossed repeatedly until a tail comes up for the first time. Write the sample space for this experiment.

A box contains 1 red and 3 black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

A pair of dice is rolled. If the outcome is a doublet, a coin is tossed. Determine the total number of elementary events associated to this experiment.

A coin is tossed twice. If the second draw results in a head, a die is rolled. Write the sample space for this experiment.

A bag contains 4 identical red balls and 3 identical black balls. The experiment consists of drawing one ball, then putting it into the bag and again drawing a ball. What are the possible outcomes of the experiment?

In a random sampling three items are selected from a lot. Each item is tested and classified as defective (D) or non-defective (N). Write the sample space of this experiment.

An experiment consists of boy-girl composition of families with 2 children.

(i) What is the sample space if we are interested in knowing whether it is boy or girl in the order of their births?

(ii) What is the sample space if we are interested in the number of boys in a family?

There are three coloured dice of red, white and black colour. These dice are placed in a bag. One die is drawn at random from the bag and rolled, its colour and the number on its uppermost face is noted. Describe the sample space for this experiment.

2 boys and 2 girls are in room P and 1 boy 3 girls are in room Q. Write the sample space for the experiment in which a room is selected and then a person.

A bag contains one white and one red ball. A ball is drawn from the bag. If the ball drawn is white it is replaced in the bag and again a ball is drawn. Otherwise, a die is tossed. Write the sample space for this experiment.

A box contains 1 white and 3 identical black balls. Two balls are drawn at random in succession without replacement. Write the sample space for this experiment.

An experiment consists of rolling a die and then tossing a coin once it number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

A die is thrown repeatedly until a six comes up. What is the sample space for this experiment.

A coin is tossed. Find the total number of elementary events and also the total number of events associated with the random experiment.

List all events associated with the random experiment of tossing of two coins. How many of them are elementary events?

Three coins are tossed once. Describe the following events associated with this random experiment:

A = Getting three heads, B = Getting two heads and one tail, C = Getting three tails, D = Getting a head on the first coin.

(i) Which pairs of events are mutually exclusive?

(ii) Which events are elementary events?

(iii) Which events are compound events?

In a single throw of a die describe the following events:

(i) A = Getting a number less than 7

(ii) B = Getting a number greater than 7

(iii) C = Getting a multiple of 3

(iv) D = Getting a number less than 4

(v) E = Getting an even number greater than 4.

(vi) F = Getting a number not less than 3.

Also, find A ∪ B, A ∩ B, B ∩ C, E ∩ F, D ∩ F and .

Three coins are tossed. Describe

(i) two events A and B which are mutually exclusive.

(ii) three events A, B and C which are mutually exclusive and exhaustive.

(iii) two events A and B which are not mutually exclusive.

(iv) two events A and B which are mutually exclusive but not exhaustive.

A die is thrown twice. Each time the number appearing on it is recorded. Describe the following events:

(i) A = Both numbers are odd.

(ii) B = Both numbers are even

(iii) C = sum of the numbers is less than 6.

Also, find A ∪ B, A ∩ B, A ∪ C, A ∩ C. Which pairs of events are mutually exclusive.

Two dice are thrown. The events A, B, C, D, E and F are describes as follows.

A = Getting an even number on the first die.

B. Getting an odd number on the first die.

C = Getting at most 5 as sum of the numbers on the two dice.

D = Getting the sum of the numbers on the dice greater than 5 but less than 10.

E = Getting at least 10 as the sum of the numbers on the dice.

F = Getting an odd number on one of the dice.

(i) Describe the following events: A and B, B or C, B and C, A and E, A or F, A and F

(ii) State true or false:

(a) A and B are mutually exclusive.

(b) A and B are mutually exclusive and exhaustive events

(c) A and C are mutually exclusive events

(d) C and D are mutually exclusive and exhaustive events

(e) C, d and E are mutually exclusive and exhaustive events

(f) A’ and B’ are mutually exclusive events

(g) A, B, F are mutually exclusive and exhaustive events

The numbers 1, 2, 3 and 4 are written separately on four slips of paper. The slips are then put in a box and mixed thoroughly. A person draws two slips from the box, one after the other, without replacement. Describe the following events:

A = The number on the first slip is larger than the one on the second slip.

B = The number on the second slip is greater than 2

C = The sum of the numbers on the two slips is 6 or 7

D = The number on the second slips is twice that on the first slip.

Which pair (s) of events is (are) mutually exclusive?

A card is picked up from a deck of 52 playing cards.

(i) What is the sample space of the experiment?

(ii) What is the event that the chosen card is a black faced card?

Which of the following cannot be valid assignment of probability for elementary events or outcomes of sample space S = {w₁, w₂, w₃, w₄, w₅, w₆, w₇}:

A die is thrown. Find the probability of getting:

(i) a prime number

(ii) 2 or 4

(iii) a multiple of 2 or 3

In a simultaneous throw of a pair of dice, find the probability of getting:

(i) 8 as the sum

(ii) a doublet

(iii) a doublet of prime numbers

(iv) an even number on first

(v) a sum greater than 9

(vi) an even number on first

(vii) an even number on one and a multiple of 3 on the other

(viii) neither 9 nor 11 as the sum of the numbers on the faces

(ix) a sum less than 6

(x) a sum less than 7

(xi) a sum more than 7

(xii) neither a doublet nor a total of 10

(xiii) odd number on the first and 6 on the second

(xiv) a number greater than 4 on each die

(xv) a total of 9 or 11

(xvi) a total greater than 8

In a single throw of three dice, find the probability of getting a total of 17 or 18

Three coins are tossed together. Find the probability of getting:

(i) exactly two heads

(ii) at least two heads

(iii) at least one head and one tail

What is the probability that an ordinary year has 53 Sundays?

What is the probability that a leap year has 53 Sundays and 53 Mondays?

A bag contains 8 red and 5 white balls. Three balls are drawn at random. Find the probability that:

(i) All the three balls are white

(ii) All the three balls are red

(iii) One ball is red and two balls are white

In a single throw of three dice, find the probability of getting the same number on all the three dice

Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is ;

(i) a black king

(ii) either a black card or a king

(iii) black and a king

(iv) a jack, queen or a king

(v) neither an ace nor a king

(vi) spade or an ace

(vii) neither an ace nor a king

(viii) a diamond card

(ix) not a diamond card

(x) a black card

(xi) not an ace

(xii) not a black card

In shutting a pack of 52 playing cards, four are accidently dropped; find the chance that the missing cards should be one from each suit

From a deck of 52 cards, four cards are drawn simultaneously, find the chance that they will be the four honors of the same suit

Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random. What is the probability that the ticket has a number which is a multiple of 3 or 7?

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that one is red, one is white and one is blue

A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random, find the probability that:

(i) both the balls are white

(ii) one ball is black and the other red

(iii) both the balls are of the same colour

A bag contains 6 red, 4 white and 8 blue balls. If three balls are drawn at random, find the probability that:

(i) one is red and two are white

(ii) two are blue and one is red

(iii) one is red

Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain:

(i) just one ace

(ii) at least one ace?

The face cards are removed from a full pack. Out of the remaining 40 cards, 4 are drawn at random. What is the probability that they belong to different suits?

There are four men and six women on the city councils. If one council member is selected for a committee at random, how likely is that it is a women?

A box contains 100bulbs, 20 of which are defective. 10 bulbs are selected for inspection. Find the probability that:

(i) all 10 are defective

(ii) all 10 are good

(iii) at least one is defective

(iv) none is defective

Find the probability that in a random arrangement of the letters of the word ‘SOCIAL’ vowels come together

The letters of the word ‘CLIFTON’ are placed at random in a row. What is the chance that two vowels come together?

The letters of the word “FORTUNATES’ are arranged at random in a row. What is the chance that the two ‘T’ come together?

A committee of two persons is selected from two men and two women. What is the probability that the committee will have (i) no man? (ii) one man? (iii) two men?

If odds in favour of an event be 2: 3, find the probability of occurrence of this event

If odds against an events be 7: 9, find the probability of non-occurrence of this event.

Two balls are drawn at random from a bag containing 2 white, 3 red, 5 green and 4 black balls, one by one without, replacement. Find the probability that both the balls are of different colours.

Two unbiased dice are thrown. Find the probability that:

(i) neither a doublet nor a total of 8 will appear

(ii) the sum of the numbers obtained on the two dice is neither a multiple of 2 nor a multiple of 3

A bag contains 8 red, 3 white and 9 blue balls. If three balls are drawn at random, determine the probability that (i) all the three balls are blue balls 9ii) all the balls are of different colours

A bag contains 5 red, 6 white and 7 black balls. Two balls are drawn at random. What is the probability that both balls are red or both are black?

If a letter is chosen at random from the English alphabet, find the probability that the letter is (i) a vowel (ii) a constant

In a lottery, a person chooses six different numbers at random from 1 to 20, and if these six numbers match with six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?

20 cards are numbered from 1 to 20. One card is drawn at random. What is the probability that the number on the cards is:

(i) a multiple of 4?

(ii) not a multiple of 4?

(iii) odd?

(iv) greater than 12?

(v) divisible by 5?

(vi) not a multiple of 6?

Two dice are thrown. Find the odds in favour of getting the sum

(i) 4 (b) 5

(iii) What are the odds against getting the sum 6?

What are the odds in favour of getting a spade if a card is drawn from a well-shuffled deck of cards? What are the odd in favour of getting a king?

A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that:

(i) al are blue?

(ii) at least one is green?

A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is (i) white (ii) white and odd numbered (iii) even numbered (iv) red or even numbered.

A class consists of 10 boys and 8 girls. Thee students are selected at random. What is the probability that the selected group has (i) all boys? (ii) all girls? (iii) 1 boy and 2 girls? (iv) at least one girl? (v) at most one girl?

Five cards are drawn from a well-shuffled pack of 52 cards. Find the probability that all the five cards are hearts.

A bag contains tickets numbered from 1 to 20. Two tickets are drawn. Find the probability that (i) both the tickets have prime numbers on them (ii) on one there is a prime number and on the other, there is a multiple of 4.

An urn contains 7 white, 5 black and 3 red balls. Two balls are drawn at random. Find the probability that 9i) both the balls are red (ii) one ball is red and the other is black (iii) one ball is white.

A and B throw a pair of dice. If A throws 9, find B’s chance of throwing a higher number

In a hand at Whist, what is the probability that four kings are held by a specified player?

Find the probability that in a random arrangement of the letters of the word ‘UNIVERSITY’, the two I’s do not come together.

If A and B be mutually exclusive events associated with a random experiment such that P(A) = 0.4 and P(B) = 0.5, then find :

(i) P(A ∪ B)

A and B are two events such that P(A) = 0.54, P(B) = 0.69 and P(A ∩ B) =0.35. Find (i) P(A ∪ B), (ii) (iii) (iv)

Fill in the blanks in the following table :

If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.4 and P(A ∪ B) = 0.5, find P(A ∩ B).

If A and B are two events associated with a random experiment such that P(A) = 0.5, P(B) = 0.3 and P(A ∩ B) = 0.2, find P(A ∪ B).

If A and B are two events associated with a random experiment such that P(A ∪ B) = 0.8, P(A ∩ B) = 0.3 and = 0.5 , find P(B).

Given two mutually exclusive events A and B such that P(A) = 1/2 and P(B) = 1/3, find P(A or B).

There are three events A, B, C one of which must and only one can happen, the odds are 8 to 3 against A, 5 to 2 against B, fins the odds against C.

One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

In a single throw of two dice, find the probability that neither a doublet nor a total of 9 will appear.

A natural number is chosen at random from amongst first 500. What is the probability that the number so chosen is divisible by 3 or 5?

A die is thrown twice. What is the probability that at least one of the two throws come up with the number 3?

A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75. What is the probability of passing the Hindi examination?

One number is chosen from numbers 1 to 100. Find the probability that it is divisible by 4 or 6?

From a well shuffled deck of 52 cards, 4 cards are drawn at random. What is the probability that all the drawn cards are of the same colour.

100 student appeared for two examinations. 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed at least one examination.

A box contains 10 white, 6 red and 10 black balls. A ball is drawn at random from the ox. What is the probability that the ball drawn is either white or red?

In a race, the odds in favour of horses A,B,C,D are 1:3, 1:4, 1:5 and 1:6 respectively. Find probability that one of the wins the race.

The probability that a person will travel by plane is 3/5 and that he will travel by train is 1/4. What is the probability that he (she) will travel by plane or train?

Two cards are drawn from a well shuffled pack of 52 cards. Find the probability that either both are black or both are kings.

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of a the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?

A box contains 30 bolts and 40 nuts. Half of the bolts and half of the nuts are rusted. If two items are drawn at random, what is the probability that either both are rusted or both are bolts?

An integer is chosen at random from first 200 positive integers. Find the probability that the integer is divisible by 6 or 8.

Find the probability of getting 2 or 3 tails when a coin is tossed four times.

Suppose an integer from 1 through 1000 is chosen at random, fins the probability that the integer is a multiple of 2 or a multiple of 9.

In a large metropolitan area, the probabilities are 0.87, 0.36, 0.30 that a family (randomly chosen for a sample survey) owns a colour television set, a black and white television set, or both kinds of sets. What is the probability that a family owns either any one or both kinds of sets?

If A and B are mutually exclusive events such that P(A) = 0.35 and P(B) = 0.45, find

(i) P (A ∪ B) (ii) P (A ∩ B)

(iii) (iv)

A sample space consists of 9 elementary event E₁, E₂, E₃, ……E₈, E₉ whose probabilities are P(E₁) = P(E₂) = 0.08, P(E₃) = P(E₄) = 0.1, P(E₆) = P(E₇) = 0.2, P(E₈) = P(E₉) = 0.07

Suppose A = {E₁, E₅, E₈}, B = {E₂, E₈, E₉}

(i) Compute P(A), P(B) and P(A ∩ B).

(ii) Using the addition law of probability, find P (A ∪ B).

(iii) List the composition of the event A ∪ B, and calcite P(A ∪ B) by adding the probabilities of the elementary events.

(iv) Calculate from P(B), also calculate directly from the elementary events of .

Three numbers are chosen at random from numbers 1 to 30. Write the probability that the chosen numbers are consecutive.

n (> 3) persons are sitting in a row. Two of them are selected. Write the probability that they are together.

A single letter is selected at random from the word ‘PROBABILITY’. What is the probability that it is a vowel?

What is the probability that a leap year will have 53 Fridays or 53 Saturday?

Three dice are thrown simultaneously. What is the probability of getting 15 as the sum?

If the letters of the word ‘MISSISSIPPI’ are written down at random in a row, what is the probability that four S’s come together.

What is the probability that the 13^th days of a randomly chosen month is Friday?

Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral.

If A and B are two independent events such that , then write the values of P(A) and P(B).

One card is drawn from a pack of 52 cards. The probability that it is the card of a king or spade is

Two dice are thrown together. The probability that at least one will show its digit greater than 3 is

Two dice are thrown simultaneously. The probability of obtaining a total score of 5 is

Two dice are thrown simultaneously. The probability of obtaining total score of seven is

The probability of getting a total of 10 in a single throw of two dice is

A card is drawn at random from a pack of 100 cards numbered 1 to 100. The probability of drawing a number which is a square is

A bag contains 3 red, 4 white and 5 blue balls. All balls are different. Two balls are drawn at random. The probability that they are of different colour is

Two dice are thrown together. The probability that neither they show equal digits nor the sum of their digits is 9 will be

Four persons are selected at random out of 3 men, 2 women and 4 children. The probability that there are exactly 2 children in the selection is

The probabilities of happening of two events. A and B are 0.25 and 0.50 respectively. If the probability of happing of A and B together is 0.14, then probability that neither A nor B happens is

A die is rolled, then the probability that a number 1 or 6 may appear is

Six boys and six girls sit in a row randomly. The probability that all girls sit together is

The probabilities of three mutually exclusive events A, B and C are given by 2/3, 1/4 and 1/6 respectively. The statement

If are the probabilities of three mutually exclusive and exhaustive events, then the set of all values of p is

A pack of cards contains 4 aces, 4 kings, 4 queens and 4 jacks. Two cards are drawn at random. The probability that at least one of them is an ace is

If three dice are thrown simultaneously, then the probability of getting a score of 5 is

One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are

The probability that a leap year will have 53 Fridays or 53 Saturdays is

A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is

A and B are two events such that P(A) = 0.25 and P(B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is

If the probability of A to fail in an examination is and that of B is . Then, the probability that either A or B fails is

A box contains 10 good articles and 6 defective articles. One item is drawn at random. The probability that it is either good or has a defect, is

Three integers are chosen at random from the first 20 integers. The probability that their product is even is

Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, is

A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomly. The probability that it is black or red ball is

Two dice are thrown simultaneously. The probability of getting a pair of sixes is

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

Five persons entered the lift cabin on the ground floor of an 8 floored house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is

A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect is

A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is

If S is the sample space and , where A and B are two mutually exclusive events, then P(A) =

One mapping is selected at random from all the mappings of the set A = {1, 2, 3, ….., n) into itself. The probability that the mapping selected is one to one is

If A, B, C are three mutually exclusive and exhaustive events of an experiment such that 3P(A) = 2P(B) = P(C), then P(A) is equal to

If A and B are mutually exclusive events then

If P (A ∩ B) = P (A ∪ B) for any two events A and B, then

Three numbers are chosen from 1 to 20. The probability that they are not consecutive is

6 boys and 6 girls sit in a row a row at random. The probability that all the girls sit together is

Without repetition of the numbers, four digit numbers are formed with the numbers 0, 2, 3, 5. The probability of such a number divisible by 5 is

If the probability for A to fail in an examination is 0.2 and that for B is 0.3, then the probability that either A or B fails is

Three digit numbers are formed using the digits 0, 2, 4, 6, 8. A number is chosen at random out of these numbers what is the probability that this number has the same digits?