### Probability Problems and Answers:

**Ques.** *A* and *B* toss a coin alternatively, the first to show a head being the winner. If *A* starts the game, the chance of his winning is

(a) 5/8

(b) 1/2

(c) 1/3

(d) 2/3

**Ques.** Two dice are thrown simultaneously. The probability of getting the sum 2 or 8 or 12 is

(a) 5/18

(b) 7/36

(c) 7/18

(d) 5/36

**Ques. **Three letters are to be sent to different persons and addresses on the three envelopes are also written. Without looking at the addresses, the probability that the letters go into the right envelope is equal to

(a) 1/27

(b) 1/9

(c) 4/27

(d) ⅙

**Ques.** Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively

(a) 1/462

(b) 1/924

(c) ½

(d) None of these

**Ques.** A problem of mathematics is given to three students whose chances of solving the problem are 1/3, 1/4 and 1/5 respectively. The probability that the question will be solved is

(a) 2/3

(b) 3/4

(c) 4/5

(d) 3/5

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**Ques.** One die and one coin are tossed simultaneously. The probability of getting 6 on die and head on coin is

(a) ½

(b) 1/6

(c) 1/12

(d) None of these

**Ques.** A coin is tossed twice. The probability of getting head both the times is

(a) ½

(b) ¼

(c) ¾

(d) 1

**Ques. **From 10,000 lottery tickets numbered from 1 to 10,000, one ticket is drawn at random. What is the probability that the number marked on the drawn ticket is divisible by 20

(a) 1/100

(b) 1/50

(c) 1/20

(d) 1/10

**Ques.** Two fair dice are tossed. Let *A* be the event that the first die shows an even number and *B* be the event that the second die shows an odd number. The two event *A* and *B* are

(a) Mutually exclusive

(b) Independent and mutually exclusive

(c) Dependent

(d) None of these

**Ques.** A bag contains 5 brown socks and 4 white socks. A man selects two socks from the bag without replacement. The probability that the selected socks will be of the same colour, is

(a) 5/108

(b) 1/6

(c) 5/18

(d) 4/9

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**Ques.** In a test an examine either guesses or copies or knows the answer to a multiple choice question with 4 choices. The probability that he makes a guess is 1/3 and the probability that he copies the answer is 1/6. The probability that his answer is correct given that he copied it is 1/8. the probability that he know the answer to the question given that he correctly answered it.

(a) 24/29

(b) 8/29

(c) 13/29

(d) none of these

**Ques.** A single letter is selected at random from the word “PROBABILITY”. The probability that the selected letter is a vowel is

(a) 2/11

(b) 3/11

(c) 4/11

(d) 0

**Ques.** 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, what is the probability that it is rusted or is a nail

(a) 3/16

(b) 5/16

(c) 11/16

(d) 14/16

**Ques.** The probability of a sure event is

(a) 0

(b) 1

(c) 2

(d) 1/2

**Ques.** A problem of mathematics is given to three students whose chances of solving the problem are 1/3, 1/4 and 1/5 respectively. The probability that the question will be solved is

(a) 2/3

(b) 3/4

(c) 4/5

(d) 3/5

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**Ques.** In a throw of a die, what is the probability of getting a number less than 7

(a) 0

(b) 1

(c) 1/2

(d) None of these

**Ques.** A man and a woman appear in an interview for two vacancies in the same post. The probability of man’s selection is 1/4 and that of the woman’s selection is 1/3. What is the probability that none of them will be selected

(a) 1/2

(b) 1/12

(c) 1/4

(d) None of these

**Ques.** A box contains 10 good articles and 6 with defects. One article is chosen at random. What is the probability that it is either good or has a defect

(a) 24/64

(b) 40/64

(c) 49/64

(d) 64/64

**Ques.** The event *A* is independent of itself if and only if P (A) =

(a) 0

(b) 1

(c) 0, 1

(d) None of these

**Ques.** The probability that a teacher will give an unannounced test during any class meeting is 1/5. If a student is absent twice, then the probability that the student will miss at least one test is

(a) 4/5

(b) 2/5

(c) 7/5

(d) 9/25

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**Ques.** The sum of two positive numbers is 100. The probability that their product is greater than 1000 is

(a) 7/9

(b) 7/10

(c) 2/5

(d) None of these

**Ques. **The probability of a sure event is**
**(a) 0

(b) 1

(c) 2

(d) ½

**Ques.** Four coins are tossed. The probability that at least one head turns up, is

(a) 1/16

(b) 1/4

(c) 15/16

(d) None of these

**Ques.** From a well shuffled pack of cards one card is drawn at random. The probability that the card drawn is an ace is

(a) 1/13

(b) 4/13

(c) 3/52

(d) None of these

**Ques.** Twenty tickets are marked the numbers 1, 2, ….. 20. If three tickets be drawn at random, then what is the probability that those marked 7 and 11 are among them

(a) 3/190

(b) 1/19

(c) 1/190

(d) None of these

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**Ques.** A bag contains 8 black and 7 white balls. Two balls are drawn at random. Then for which the probability is more

(a) Both balls are white

(b) One ball is white and one is black

(c) Both balls are black

(d) All of the above are equals

**Ques. **A coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows 6 is

(a) ⅛

(b) 1/12

(c) ½

(d) 1

**Ques.** Two friends *A* and *B* have equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of *A* and *B*. The probability that all the tickets go to daughters of *A* is 1/20. The number of daughters each of them have is

(a) 4

(b) 5

(c) 6

(d) 3

**Ques. **Two cards are drawn from a pack of 52 cards. What is the probability that at least one of the cards drawn is an ace

(a) 33/221

(b) 188/221

(c) 1/26

(d) 21/221

**Ques.** Five digit numbers are formed using the digits 1, 2, 3, 4, 5, 6 and 8. What is the probability that they have even digits at both the ends

(a) 2/7

(b) 3/7

(c) 4/7

(d) None of these

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**Ques. **The probability of getting a total of 5 or 6 in a single throw of 2 dice is

(a) ½

(b) ¼

(c) ⅓

(d) ⅙

**Ques.** Two numbers are selected at random from 1, 2, 3 ……100 and are multiplied, then the probability correct to two places of decimals that the product thus obtained is divisible by 3, is

(a) 0.55

(b) 0.44

(c) 0.22

(d) 0.33

**Ques. **In a single throw of two dice the probability of obtaining an odd number is

(a) ⅙

(b) ½

(c) ⅓

(d) None of these

**Ques.** A party of 23 persons take their seats at a round table. The odds against two persons sitting together are

(a) 10 : 1

(b) 1 : 11

(c) 9 : 10

(d) None of these

**Ques.** In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

(a) At least 30

(b) At most 20

(c) Exactly 25

(d) None of these

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**Ques. **The probability of an event *A* is 0.5 and that of *B* is 0.3. If *A* and *B* are mutually exclusive events, then the probability of happening neither *A* nor *B* is

(a) 0.6

(b) 0.2

(c) 0.21

(d) None of these

**Ques. **If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is

(a) 13/32

(b) ¼

(c) 1/32

(d) 3/16

**Ques. **If a dice is thrown twice, then the probability of getting 1 in the first throw only is

(a) 1/36

(b) 3/36

(c) 5/36

(d) ⅙

**Ques.** Two coins are tossed. Let *A* be the event that the first coin shows head and *B* be the event that the second coin shows a tail. Two events *A* and *B* are

(a) Mutually exclusive

(b) Dependent

(c) Independent and mutually exclusive

(d) None of these

**Ques.** Three squares of a chess board are chosen at random, the probability that two are of one color and one of another is

(a) 16/21

(b) 8/21

(c) 32/12

(d) None of these

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**Ques.** Out of 40 consecutive natural numbers, two are chosen at random. Probability that the sum of the numbers is odd, is

(a) 14/29

(b) 20/39

(c) 1/2

(d) None of these

**Ques.** Two squares are chosen at random on a chess-board. The probability that they have a side in common, is

(a) 1/9

(b) 2/7

(c) 1/18

(d) None of these

**Ques.** Three distinct numbers are selected from the first 100 natural numbers. The probability that all the three numbers are divisible by 2 and 3 is

(a) 4/25

(b) 4/35

(c) 4/55

(d) 4/1155

**Ques. **Two cards are drawn one by one at random from a pack of 52 cards. The probability that both of them are king, is

(a) 2/13

(b) 1/169

(c) 1/221

(d) 30/221

**Ques.** Out of 21 tickets marked with numbers from 1 to 21, three are drawn at random. The chance that the numbers on them are in A.P., is

(a) 10/133

(b) 9/133

(c) 9/1330

(d) None of these

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**Ques.** If *A* and *B* are mutually exclusive events, then the value of *P *(*A *or *B*) is

(a) 0

(b) –1

(c) 1

(d) None of these

**Ques.** A pair of fair dice is rolled together till a sum of either 5 or 7 is obtained. Then the probability that 5 comes before 7 is

(a) 1/5

(b) 2/5

(c) 4/5

(d) None of these

**Ques. **Two dice are thrown. The probability that the sum of numbers appearing is more than 10, is

(a) 1/18

(b) 1/12

(c) ⅙

(d) None of these

**Ques.** A determinant is chosen at random. The set of all determinants of order 2 with elements 0 or 1 only. The probability that value of the determinant chosen is positive, is

(a) 3/16

(b) 3/8

(c) 1/4

(d) None of these

**Ques.** If from each of the three boxes containing 3 white and 1 black, 2 white and 2 black, 1 white and 3 black balls, one ball is drawn at random, then the probability that 2 white and 1 black ball will be drawn is

(a) 13/32

(b) 1/4

(c) 1/32

(d) 3/16

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**Ques.** An unbiased die is tossed until a number greater than 4 appears. The probability that an even number of tosses is needed is

(a) 1/2

(b) 2/5

(c) 1/5

(d) 2/3

**Ques.** Two persons ‘*A*’ and ‘*B*’ have respectively n + 1 and *n* coins which they toss simultaneously. Then the probability that *A* will have more heads than *B* is

(a) ½

(b) > ½

(c) < ½

(d) None of these

**Ques. **There are two children in a family. The probability that both of them are boys is

(a) ½

(b) ⅓

(c) ¼

(d) None of these

**Ques.** Three coins are tossed together, then the probability of getting at least one head is

(a) 1/2

(b) 3/4

(c) 1/8

(d) 7/8

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

(a) 2/3

(b) 1/2

(c) 3/4

(d) 1/3

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**Ques.** A bag *x* contains 3 white balls and 2 black balls and another bag *y* contains 2 white balls and 4 black balls. A bag and a ball out of it are picked at random. The probability that the ball is white, is

(a) 3/5

(b) 7/15

(c) 1/2

(d) None of these

**Ques.** A man alternately tosses a coin and throws a dice beginning with the coin. The probability that he gets a head in the coin before he gets a 5 or 6 in the dice is

(a) 3/4

(b) 1/2

(c) 1/3

(d) None of these

**Ques. **A dice is thrown twice. The probability of getting 4, 5 or 6 in the first throw and 1, 2, 3 or 4 in the second throw is

(a) 1

(b) ⅓

(c) 7/36

(d) None of these

**Ques.** The probability of getting at least one tail in 4 throws of a coin is

(a) 15/16

(b) 1/16

(c) 1/4

(d) None of these

**Ques.** A fair coin is tossed *n* times. Let *X* be the number of times head is observed. If P(X = 4), P(X = 5) and P(X = 6) are in H.P., then *n* is equal to

(a) 7

(b) 10

(c) 14

(d) None of these

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**Ques.** A committee of five is to be chosen from a group of 9 people. The probability that a certain married couple will either serve together or not at all, is

(a) 1/2

(b) 5/9

(c) 4/9

(d) 2/9

**Ques.** A card is drawn at random from a pack of cards. The probability of this card being a red or a queen is

(a) 1/13

(b) 1/26

(c) 1/2

(d) 7/13

**Ques. **The probability of happening an event A in one trial is 0.4. The probability that the event A happens at least once in three independent trials is

(a) 0.936

(b) 0.784

(c) 0.904

(d) 0.216

**Ques.** The probability of getting a number greater than 2 in throwing a die is

(a) 1/3

(b) 2/3

(c) 1/2

(d) 1/6

**Ques.** For an event, odds against is 6 : 5. The probability that event does not occur, is

(a) 5/6

(b) 6/11

(c) 5/11

(d) 1/6

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**Ques.** One hundred identical coins each with probability *p* of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of *p* is

(a) 1/2

(b) 49/101

(c) 50/101

(d) 51/101

**Ques.** A box contains 10 red balls and 15 green balls. If two balls are drawn in succession then the probability that one is red and other is green, is

(a) 1/3

(b) 1/2

(c) 1/4

(d) None of these

**Ques. **Two dice are thrown simultaneously. What is the probability of obtaining a multiple of 2 on one of them and a multiple of 3 on the other?**
**(a) 5/36

(b) 11/36

(c) ⅙

(d) ⅓

**Ques.** A box contains 100 tickets numbered 1, 2 …… 100. Two tickets are chosen at random. It is given that the maximum number on the two chosen tickets is not more than 10. The minimum number on them is 5 with probability

(a) 1/8

(b) 13/15

(c) 1/7

(d) None of these

**Ques.** A five digit number is formed by writing the digits 1, 2, 3, 4, 5 in a random order without repetitions. Then the probability that the number is divisible by 4 is

(a) 3/5

(b) 18/5

(c) 1/5

(d) 6/5

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**Ques.** Two dice are rolled one after the other. The probability that the number on the first is smaller than the number on the second is

(a) ½

(b) 7/18

(c) ¾

(d) 5/12

**Ques. **If three coins are tossed simultaneously, the probability of getting at least one head

(a) 1/8

(b) 3/8

(c) 1/2

(d) 7/8

**Question: **A fair dice is tossed two times. The probability that the second toss results in a value that is higher than the first toss is

(a) 2/36

(b) 2/6

(c) 5/12**
**(d) 1/2