2) if a coin is tossed, what is the chance of a tail ? If three coins are tossed, find the probability that they are all tails. 1/2, 1/8
3) From a pack of 52 cards, one cards is drawn at random. Find the chance drawing a spade and also not drawing a spade. 1/4, 3/4
4) Two unbiased dice are thrown together, find the probability of obtaining 2 in both the dice. 1/36
5) if a dice is tossed, what is the chance of getting
A) an even number. 1/2, 2/3, 1/3
B) a number greater than 2.
C) an even number greater than 2?
6) From a pack of 52 cards, one card is drawn at random. Find the chance that the card is
A) red. 1/2
B) an ace. 1/13
C) an spade. 1/4
C) either king or an ace. 2/13
7) What is the chance of picking a spade, or an ace not of spade, from a pack of 52 cards ? 4/13,
8) out of 5 players of which 2 are members of a certain club, 3 are to be selected to represent the country at an international tournament, Find the probability that less than two of those selected to represent are members of the club. 7/10
9) From a well shuffled pack of 52 cards, one card is drawn at random, Find the chance that the card is
A) neither a king or a knave.
B) neither a king nor a knave
C) neither a heart nor a diamond.
D) neither an ace, nor a king, nor a queen, nor a knave. 2/13, 11/13, 1/2 , 9/13
10) Two letters are drawn at random from the HOME. Find the probability
A) both the letters are vowels. 1/6
B) at least one is a vowel. 5/6
C) one of the letters chosen is M. 1/2
11) From a bag containing 7 white and 5 red balls, 4 balls are drawn at random. What is the probability that they are all are white ? 7/99
12) In a single cast with two dice, find the probability of throwing 7( i.e., of throwing two numbers whose sum is 7). 1/6
13) If 4 unbiased coins are tossed, find the probability that there should be two heads. 3/8
14) Find the chance of throwing at least 8 in a single cast with two dice .
15) two balls are drawn at random from a bag containing 6 white balls and 4 Black balls. find the chance that one is white and other is black. 8/15
16) 4 balls are drawn at random from a bag containing 5 red and 7 white balls. compute the probability of getting
A) 4 red balls. 1/99
B) two Red and two white balls. 14/34
C) three white balls and 1 red ball. 35/99
17) four balls are drawn at random from a bag containing 5 black and 8 white balls. What are the odds in favour of the balls being all white. 14: 129
18) find the chance of not throwing an ace, two or three, in the single throw with a die. 1/2
19) there are 17 balls numbered from 1 to 17 in a bag, if a person selects one at random, what is the probability that the number printed on the ball will be an even number greater than 9 . 4/17
20) what are the odds against throwing ace or 6 in a single throw with die ? and what are the odds in favour? 2:1, 1:2
21) Given are the weekly wages (in ₹) of workers in a factory: 62, 90, 78, 85, 79 and 68. If two of these workers are selected at random to serve as representatives, what is the probability that at least one will have a wage lower than the average. 3/5
22) four men in a company of 10 employees are engineers. If two men are selected random, then find the probability that atleast one of them will be an engineer. 2/3
23) five men in a company of 20 are graduate6. If 3 men are picked out of the 20 at random, What is the probability that
A) they are all graduates. 1/114
B) there is no graduate. 91/228
C) atleast one graduate ? 137/228
24) A bag contains 10 rupees coin5, 7 fifty paise coins and 4 twenty five paise coins. Find the probability of drawing
A) a rupee coin. 10/21
B) 3 rupee coins. 12/133
C) 3 coins, one of each type. 4/19
25) consider four events: A, NOT A, B, NOT B. it is given that P(B)= 0.4, P(A but NOT B)= 0.3, P(NOT A)= 0.7. find P(A UB). 0.7
26) A, B and C are three mutually exclusive events. Fi6P(B), If 1/3 P(C)= 1/2 P(A)= P(B). 1/6
27) the probability that the teacher in Statistics will take a sudden test on any day of a week is 2/5. A student abstain for 2 days in a week. what is the probability that he will miss atleast one test ? 16/25
28) An urn contains 13 balls numbering from 1 to 13. Find the probability that a ball is selected at random is a ball with number that is a multiple of three or four. 6/13
29) Find the chance of throwing at least 9 in a single case with two dice . 5/18
30) Two fair dice thrown simultaneously. The two scores are then multiplied together. Calculate the probability that the product is
A) 12. 1/9
B) even. 3/4
31) In a lot of 20 articles, 5 are defective, 4 articles the drawn at random from the lot. Find the probability that exactly two of drawn articles are defective. 70/323
32) Two cards are drawn from a well shuffle pack of 52 cards. Find the probability that
A) both are spades. 1/17
B) both are kings. 1/221
C) one is spade and the other is a heart. 13/102
33) A Sub-committee of 6 members is be formed out of a group consisting of 7 gentlemen and 4 ladies. Calculate the probability that the sub-committee will consist of
A) exactly two ladies. 5/11
B) at least two ladies. 53/66
34) an article manufactured by a company consists of two parts, A and B, in the process of manufacture of part A, 9 out of 100 are likely to be defective. similarly, 5 out of 100 are likely to be defective in the manufacture of part B. Calculate the probability that the assembled article will not be defective. 0.8645
35) the manufacturing process of an article consists of two parts X and Y. the probabilities of defect in parts X and Y are 10% and 15% resp6. What is the probability that the assembled products will not have any defect ? 0.765
36) there are four balls in a bag-- white, red and green and blue. If a bell is drawn out at random three times in succession, what is the chance that all the three would be white? (Assume that the ball is replaced after each drawing). 1/64
37) a box contain 9 red and 6 white balls. Two balls are drawn at random one after another. Find the probability that the both the balls are white, when the first draw ball is not replaced before the second drawing. 1/7
38) a coin is tossed 3 times in succession. what is the probability of the tosses coming in the order.
A) head, tail and head. 1/8
B) head, head, head. 1/8
C) two heads and one tail. 1/8
39) From a bag containing 5 green, 6 blue and 4 red balls, 7 balls are drawn at random. find the chance that 2 green, 3 blue and 2 red balls are drawn. What are the odds against drawing 2 green, 3 blue and 2 red balls. 80/429, 349:89
40) If a die is throwing twice, what is the probability that the first throw does not show less than 4 and the second does not show more than 4 1/3
41) A pair of dice are thrown. Find the probability of getting a sum of 7, when it is known that the digit in the first die is greater than that of the second.
42) in a single cast with two dice
A) what are the odds against throwing 8, i e. Against two numbers the sum of which is 8 ? 31:5
B) what is the chance of throwing more than 8, and what is the probability of throwing less than 8. 5/18, 7/12
C) find the probability of throwing atleast 8 in a single cast with two dice. 5/12
43) In a single cast with 3 dice, what is the probability of throwing
A) three fives.
B) two-four-six.
C) five-six-six ?
What are the odds against the events. 1/216, 215:1, 1/36, 35:2, 1)72, 71:1
44) Three cards are drawn from a pack of 52 cards, each card being replaced before the next one is drawn. compute the probability that all are
A) spades. 1/64
B) aces. 1/2197
C) red. 1/8
45) One bag contains 4 red and 2 black balls, another bag contains 3 red and five black balls. if one ball is drawn from each bag, determine the probability that
A) both are red. 1/4
B) both are black. 5/24
C) one is red and one is black. 13/24
46) box A contains 4 white and 3 red balls while box B contains 5 white and 4 red balls. If one ball is drawn at random from each box, what is the probability that both the balls are of the same colour? 32/63
47) One counter foil is drawn at random from the bag containing 70 counter foils marked with the first 70 numerals. Find the chance that it is multiple of 8 ton 9. 3/14
48) From a set of 18 balls marked 1,2,3,......17, 18, one is drawn at random. What is the chance that its number is either multiple of 3 or 4 ? 1/2
49) An investment consultant predicts the odd against the price of a certain stock will go up during next week by 2:1 and the odd in favour of the price remaining same by 1 : 3. What is the probability that the price of the stock will go down during the next week? 5/12
50) A bag contains 4 green and red balls is drawn at random and then, without replacing it, a second ball is drawn. What is the chance that a green ball is drawn each time ? 2/15
51) Two drawing, each of 4 balls, are made from a bag containing 6 red and 5 black balls, the balls not being replaced before the second trial, Find the chance of the first drawing gives 4 red balls and second gives 1 red and 3 black balls. 2/3
52) A problem in statistics is given to three students A, B, C whose chances of solving it are 1/3, 1/4, 1/5 respectively. What are the probability that the problem will be solved ? 3/5
53) the probability of solving a problem by 3 students A,B, C are 2/7, 3/8 and 1/2 respectively. if each of them tries independently, find the probability that the problem is solved. find also the probability that the problem could not be solved. 87/112,25/112
54) the independent probability that the three sections of a costing department will encounter a computer error are 0.1, 0.3, 0.3, each week respectively. Calculate the probability that there will be,
A) at least one computer error. 0.559
B) 1 only one computer error encounted by the costing department next week. 0.427
55) a bag contains 4 red and 3 blue balls. Two drawing of two balls are made. Find the probability of a drawing first 2 red balls and second 2 blue balls
A) if the balls are returned to the bag after the first draw. 2/49
B) if the balls are not returned after the first draw. 3/25
56) if 20 dates and named at random, find the chance that 5 of them will be Sundays. 29C5 x 6¹⁵/7¹⁰
57) two urns contains 3 white, 7 red, 15 black and 10 white, 6 red, 9 black balls respectively. one ball is drawn from each urn. Find the probability that both the balls are of the same colour. 207/625
58) 10 balls are distributed at random among 3 boxes. what is the probability that the first box will contain three balls ? 5120/19683
59) If P(A)= 1/4, P(B)= 2/5, find P (A U B), when find A and B are two independent events. 11/20
60) If P(A)= 1/3, P(B)= 2/2, find P (A ^ B)=1/4 find P(B/A) AND P(A' ^ B'),, where A' and B' are the compliments of events A and B respectively. 3/4, 5/12
61) if the two events A and B are mutually independent and P(A)= 0.3, P(B)= 0.1, find P(A U B). 0.37
62) A speaks the truth 3 times out of 5 and B speaks the truth 5 times out of 7. What is the probability that they will contradict each other in stating the same fact ? 16/35
63) If P(A)= 1/4, P(B)= 2/5, find P (A U B) = 1/2, Find P(A^ B), P(A/B) , P(B/A). 3/20,3/8,3/5
64) If A and B be events with P(A + B)= 1/4, P(A)= 2/3 and P(AB)= 1/4, find P (A), Find P(B), P(AB). 1/3 , 2/3,3/4
65) If P(A)= 1/2, P(B)= 2/5, find P (A ^ B) = 1/3, Find P(AU B), P(A' ^/') , P(A' U/B'), P(A ^ B') , P(A' ^ B). 23/30,7/30,2/3, 1/6, 4/15
66) If P(A)= 2/3, P(B)= 1/2, find P (A U B) = 1, Find P(A/B), P(A/B') , P(B?A' ^ B'). 1/3, 1, 0
67) A construction company is bidding for two contracts, A and B. the probability that the company will get contract A is 3/5, the probability that the company will get contact B is 1/3 and the probability that the company will get both the contract the 1/8, what is the probability that company will get at least one contract ? 97/120
68) The probability that a contractor will get an electric contract is 3/5, and the probably that he will not get a plumbing contract is 7/10. If the probability of getting atleast one contract is 4/7, what is the probability the company that he will get both the contracts. 23/70
69) the probability that a management account's job applicant has a postgraduate degree is 0.30, that he has had some work experience as a chief accountant is 0.70, and that he has both is 2.0. Out of 400 applicants, what number would have either a post graduate degree of some professional work experience or both ? 320
70) A bag contains 10 red and 6 green balls. Two successive drawings of 3 balls are made without replacement. Find the probability that the first drawing will get 3 red balls and second will give 3 Green balls. 15/1001
71) A bag contains 6 white and 9 black balls. 4 balls are drawn at a time. Find the probability for the first draw to give 4 white balls and the second to give 4 black balls when the balls are not replaced before the second draw. 3/715
72) a bag contains 5 red and 3 black balls, and the second bag contains 4 red and 5 black balls. one of these is selected at random and a draw of two balls is made from it. what is the probability that one of them is red and other is black. 275/504
73) There are 2 identical boxes containing 5 white and 3red balls and 4 white and 6 red balls. A box is choosen at random and a ball is drawn from it. If the ball is white, what is the probability that it is from the second box ? 16/41
74)In a bolt factory, machines X, Y, Z manufacture respectively 20, 35, and 45 percentage of the total output. If their output 8, 6 and 5% respectively are defective bolts. One bolt is drawn randomly from the product and is found to be defective. what is the probability that it is manufactured in the machine Z ? 45/119
75) a box containing for defaction 6 electronic calculator to calculate the don out of one by one without replacement what is the probability to calculate so Drone or good one on the two calculated the probability there are two identical earns containing respectively for white 3 red balls and what three wise and 7 balls an earn is chosen A triant Time In A ball is done from it find the probability that a ball is white if the ball Drone is white what is the probability the first ear two balls I don't want after another from a back on turning three wide 5 block balls what is the probability that the first ball is white in the second is black one ball is whiten the other is black one and contents to White two black ball a second and contents to White and four black balls if one ball is chosen from each other what is the probability that there will be of the same colour for early selected at random and one ball is drawn from it what is the probability that will be avoid Paul X and Y stands in a line to random with other persons what is the probability that there are 3% why given that independent what is the probability that a leap year selected in random will content 53 Sunday and only pure selected 53 sector in a group of equal number of man 10% man in 45% on an RM unemployed what is the probability the person selected random employed contents for white 5 black balls second hand contents 5 black balls 1 ball is transpord from passed through ball is drawn from the second ear what is the probability that it is right two girls and two boys and three boys and one girl one child selected random Pradeep group show that chance that the three selection consist of one girl into boys is 1332 speak the truth in 60% of being 75% what percent of the cases are they likely to contradict Each Other is starting the same pack a 6 phase dice is so bias that is twice as likely to Sona even number as an odd number when Throne it is thrown twice what is the probably that the sum of the two number soon is given ABC in order to Toss a Coin the first wins what are the respective chances of winning has winning the game the content indefinitely from the pack of 52 cards and even numbers of card is drawn so that the probability this consist of half rate and half black cards NB throws a pair of dice a wise if we 36 ball before be throw seven so that the chance of winning age there are three mens aged 6065 and 70 years the probability to leave 5 years more than 0.84 a 60 years old 0.6% 5 years old 0.3.70 years old person find the probably that at least two obtained persons will remain alive yourself a bag contains 5.5 block balls A ball is Donald Trump on the bag and out into the bag which contains 3 what is the what is the probability can the following represent measure the probability where sample space mutual exclusive event three fare coins are tossed construct the sample space out comes at the random experiment mention two mutual exclusively find the probability one tell apan Bihar event of connected with random experiment such that let A and B wents I find let Ab To events connected the random experiment such that three the nine digit 123456789 are arranged random order to form a 9 digit number find the probability that one two three appears in the neighbours in orders men set in a family therefore children find the probability that all of them will have different Birthday to up them will have same birthday one year 365 day the back contest from the bag and put and the bag which contain three red in 7 black balls A ball is Don randomly from the second bag what is the probability that it is rate on sort expired from each of 38 BC do not the event that is target inside by the first second and the third cons respectively that ABC and mutual Independent event that find the probability register what is the chance of getting at least one defective items are drawn randomly from the lord of content items 5% room find the probability that at least two of them will have the same birthday in the same calendar month of year Mr X is called interviews for 3 separate post at the first interview there are 5 candidates at the second four candidates at the third six candidate the selection of each candidate Polytechnic find the probability that mixture X will be selected for at least one post at least two pole it was found that a large match in football supporter the Clever what is the probability that correct result a back on 10 3 8 5 8 balls in a second Back contains 48 6.41 ball is done at random proposed Baigan second back now a ball is a Drone at random from the second find the probability that it is rate
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