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Probability is a numerical description of how likely an event is to occur or how likely it is that a proposition is true. Probability is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility, and 1 indicates certainty.
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Videos on Probability
Probability – 7 Tricks to solve problems on Balls and bagsPart 1
Probability – 7 Tricks to solve problems on Balls and bagsPart 2
Please Read the below formula and concept every time before you start to solve the questions.
 Experiment: An operation which can produce some welldefined outcomes is called an experiment.
 Random Experiment: An experiment in which all possible outcomes are known and the exact output cannot be predicted in advance is called a random experiment.Examples:
 Rolling an unbiased dice.
 Tossing a fair coin.
 Drawing a card from a pack of wellshuffled cards.
 Picking up a ball of a certain colour from a bag containing balls of different colours.
 When we throw a coin, then either a Head (H) or a Tail (T) appears.
 A dice is a solid cube, having 6 faces, marked 1, 2, 3, 4, 5, 6 respectively. When we throw a die, the outcome is the number that appears on its upper face.
 A pack of cards has 52 cards. It has 13 cards of each suit, name Spades, Clubs, Hearts and Diamonds. Cards of spades and clubs are black cards. Cards of hearts and diamonds are red cards. There are 4 honours in each unit. There are Kings, Queens and Jacks. These are all called face cards.
 Sample Space: When we perform an experiment, then the set S of all possible outcomes is called the sample space.Examples:
 In tossing a coin, S = {H, T}
 If two coins are tossed, the S = {HH, HT, TH, TT}.
 In rolling a dice, we have, S = {1, 2, 3, 4, 5, 6}.
 Event: Any subset of a sample space is called an event.
 The probability of Occurrence of an Event: Let S be the sample and let E be an event. Then, E S.
P(E) = n(E) . n(S)  Results on Probability:
 P(S) = 1
 0 P (E) 1
 P() = 0
 For any events A and B we have : P(A B) = P(A) + P(B) – P(A B)
 If A denotes (notA), then P(A) = 1 – P(A).
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Question 1 of 59
1. Question
In throwing a fair dice, what is the probability of getting the number ‘3’?
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Question 2 of 59
2. Question
What is the chance of throwing a number greater than 4 with an ordinary dice whose faces are numbered from 1 to 6?
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Question 3 of 59
3. Question
Find the chance of throwing at least one ace in a simple throw with two dice.
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Question 4 of 59
4. Question
Find the chance of drawing 2 blue balls in succession from bef containg 5 red and 7 blue balls, if the balls are not being replaced.
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Question 5 of 59
5. Question
From a pack of 52 cards, two are drawn at random. Find the chance that one is knave and the other a queen.
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Question 6 of 59
6. Question
If a card is picked up at random from a pack of 52 cards. Find the probability that it is a spade.
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Question 7 of 59
7. Question
Three coins are tossed. What is the probability of getting 2 tails and 1 head?
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Question 8 of 59
8. Question
Three coins are tossed. What is the probability of getting neither 3 heads nor 3 tails?
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Question 9 of 59
9. Question
For the above question, the probability that there is at least one tail is:
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Question 10 of 59
10. Question
Two fair dice are thrown. Find the probability of getting a prime number less than 8.
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Question 11 of 59
11. Question
A bag contains 3 green and 7 white balls. Two balls are drawn from the bag in succession without replacement. What is the probability that both are white?
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Question 12 of 59
12. Question
100 students 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 failed in both the examinations?
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Question 13 of 59
13. Question
What is the probability of throwing a number greater than 2 with a fair dice?
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Question 14 of 59
14. Question
Three cards numbered 2,4 and 8 are put into a box. If a card is drawn at random, what is the probability that the card drawn is a prime number?
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Question 15 of 59
15. Question
Two fair coins are tossed. Find the probability of obtaining 2 heads
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Question 16 of 59
16. Question
In rolling two dices, find the probability that there is at least one ‘6’
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Question 17 of 59
17. Question
From a bag containing 4 white and 5 black balls man draws 3 at random. What are the odds against these being all black?
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Question 18 of 59
18. Question
Amit throws three dice in a special game of ludo. If it is known that he needs 15 or higher in this through to win then find the chance of his winning the game.
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Question 19 of 59
19. Question
Find out the probability of forming 187 or 215 with the digits 1,2,3,4,5,6,7,8,9 when only numbers of three digits are formed and when repetitions are not allowed
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Question 20 of 59
20. Question
Two balls are to be drawn from a bag containing 8 grey and 3 blue balls. Find the chance that they will both be blue.
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Question 21 of 59
21. Question
Two fair dices are thrown. Given that the3 sum of the dice is less than or equal to4, find the probability that only one dice shows two.
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Question 22 of 59
22. Question
If 8 coins are tossed, what is the chance that one and only one will turn up head?
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Question 23 of 59
23. Question
What is the chance that a leap year, selected at random, will contain 53 Sundays?
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Question 24 of 59
24. Question
Two dice are thrown. If the total on the faces of the two dices are 6, find the probability that there are two odd numbers on the faces?
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Question 25 of 59
25. Question
Amaranth appears in an exam that had four subjects. The chance he passes an individual subject’s test is 0.8 what is the probability that he will pass in all subject?
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Question 26 of 59
26. Question
A speaks the truth 3 out of 4 times, and B 5 out of 6 times. What is the probability that they will contradict each other in stating the same fact?
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Question 27 of 59
27. Question
A party of n persons sits at round table. Find the odds against two specified persons sitting next two each other.
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Question 28 of 59
28. Question
If 4 whole numbers are taken at random and multiplied together, what s the chance that thelast digit in the product is 1,3,7 or 9?
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Question 29 of 59
29. Question
In four throws with a pair of dices what is the chance of throwing a double twice?
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Question 30 of 59
30. Question
A fair dice is tossed six times. Find the probability of getting a third six on the six throw.
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Question 31 of 59
31. Question
Seven whitee balls and three black balls are randomly placed in a row. Find the probability that no two black balls are placed adjacent to each other.
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Question 32 of 59
32. Question
A fair coin is tossed repeatedly. If head appears on the first four tosses then the probability of appearance of tail on the fifth toss is
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Question 33 of 59
33. Question
The letters of word ‘article’ are arranged at random. Find the probability that the vowels may occupy the even places.
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Question 34 of 59
34. Question
What is the probability that four Ss come consecutively in the word MISSISSIPI?
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Question 35 of 59
35. Question
A bag contain 8 white and 4 red balls. 5 balls are drawn at random. What is the probability that two of them are red and three are white?
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Question 36 of 59
36. Question
A team of 4 is to be constituted out of 5 girls and 6 boys. Find the probability that the team may have 3 girls.
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Question 37 of 59
37. Question
12 persons are seated around the round table . what is the probability that two particular persons sit together.
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Question 38 of 59
38. Question
Six boys and six girls sit in a row randomly. Find the probability that all the six girls sit together.
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Question 39 of 59
39. Question
From a group of 7 man and 4 women a committee of 6 persons is formed. What is the probability that the committee will consist of exactly two women?
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Question 40 of 59
40. Question
A bag contains 5 red, 4 green and three black balls . if three balls are drawn out of it at random, find the probability of drawing exactly 2 red balls.
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Question 41 of 59
41. Question
Out of a pack of 52 cards 1 is lost; from the remainder of the pack, two cards are drawn and are found to be spades. Find the chance that the missing card is a spade.
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Question 42 of 59
42. Question
A pair of fair dice are rolled together till a sum of either 5 or 7 is obtained. The probability that 5 comes before 7 is
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Question 43 of 59
43. Question
What is the probability of the destruction of the bridge if only 5 bombs are dropped?
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Question 44 of 59
44. Question
Six blue balls are put in three boxes. The probability of putting balls in the boxes in equal numbers is
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Question 45 of 59
45. Question
Three numbers are chosen at random without replacement from (1,2,3……10). The probability that the minimum number is 3 or the maximum number is 7 is
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Question 46 of 59
46. Question
There are 5 envelopes corresponding to 5 letters. If the letters are placed in the envelopes at random, what is the probability that all the letters are not placed in the right envelopes?
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Question 47 of 59
47. Question
Six boys and six girls sit in a row at random. Find the probability that the boys and girls sit alternately.
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Question 48 of 59
48. Question
A and B throw a pair of dice alternately. A wins if he throws 6 before B throws 5 and B wins if he throws 5 before A throw 6. Find B’s chance of winning if A makes the first throw.
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Question 49 of 59
49. Question
Two persons A and B toss a coin alternately till one of them gets head and wins the game. Find B’s chance of winning if A tosses the coin first.
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Question 50 of 59
50. Question
A bag contains 5 black and 3 red balls. A ball is taken out of the bag and is not returned to it. If this process is repeated three times, then what is probability of drawing a black ball in the next draw of a ball?
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Question 51 of 59
51. Question
For question 13, what is the probability of drawing a red ball?
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Question 52 of 59
52. Question
There are 10 pairs of socks in a cupboard from which 4 individual socks are picked at random. The probability that there is at least one pair is.
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Question 53 of 59
53. Question
A fair coin is tossed 10 times. Find the probability that two heads do not occur consecutively.
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Question 54 of 59
54. Question
In a room there are 7 persons. The chance that two of them were born on the same day of the week is
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Question 55 of 59
55. Question
In a hand at a game of bridge, what is the chance that the 4 kings are held by a specified player?
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Question 56 of 59
56. Question
One hundred identical coins each with probability P of showing up heads are tossed once. If 0
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Question 57 of 59
57. Question
Two small squares on a chess board are chosen at random. Find the probability that they have a common side:
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Question 58 of 59
58. Question
Two small squares on a chess board are chosen at random. Find the probability that they have a common side:
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Question 59 of 59
59. Question
30 monkeys went to a picnic. 25 monkeys chose to irritate cows while 20 chose to irritate buffaloes. How many chose to irritate both buffaloes and cows?
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