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DOWNLOAD MOBILE APPLICATION TO LEARN MORE: PROBABILITY FOR JEE MAINS QUESTIONS
DOWNLOAD MOBILE APPLICATION TO LEARN MORE: PROBABILITY FOR JEE MAINS QUESTIONS
Table of Contents
PROBABILITY FOR JEE MAINS QUESTIONS
1. Two numbers are selected randomly from the set S = {1, 2, 3, 4, 5, 6} without replacement. The probability that minimum of the two numbers is less than 4 is
2. An urn contains n white balls numbered 1 to n, n black balls numbered 1 to n and n red balls numbered 1 to n. If two balls are drawn without replacement, then the probability, that they are of the same colour or bear the same number, is
3. A man alternately tosses a fair coin and throws a fair die beginning with the coin. The probability, that he gets a head in the coin before he gets 5 or 6 in the die, is
4. A and B throw a die each. The probability, that A’s throw is not greater than B’s throw, is
5. A card is drawn from a pack of playing cards. What is the probability that it will be either a king of diamond or a queen of heart.
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6. Five dice are tossed. What is the probability that the five numbers shown be different ?
7. If the events A and B are independent and if
8. One die of red colour (R) one of white colour (W) and one of blue colour (B) are placed in a bag. One die is selected at random and rolled, its colour and the number on its uppermost face is noted. Then, the sample space is
(c) Both (a) and (b)
(d) none of these
9. A coin is tossed twice. If the second throw result in a tail, a die is thrown. Then, the total number of the outcomes of this experiment
(a) 11
(b) 13
(c) 14
(d) 16
10. From the employees of a company, 5 persons are selected to represent them in managing committee of the company. Particulars of five person are as follows
| S.No. | Name | Sex | Age (in Years) |
| 1. | Harish | M | 30 |
| 2. | Rohan | M | 33 |
| 3. | Sheetal | F | 46 |
| 4. | Alis | F | 28 |
| 5. | Salim | M | 41 |
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A person is selected at random from this group to act as a spokes person. What is the probability that the spokes person will be either male or over 35 year?
(d) none of these
11. A natural number x is chosen at random from the first 100 natural numbers. The probability that
(d) none of these
12. A die is thrown. Let A be the event that the number obtained is greater than 3 and B be the event that the number obtained is less than 5.Then,
(c) 0
(d) 1
13. Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only, if the first misses the target. The probability that the target is hit by the second plane, is
(a) 0.06
(b) 0.14
(c) 0.32
(d) 0.7
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14. Among 15 players, 8 are batsmen and 7 are bowlers. The probability that the team is chosen of 6 batsmen and 5 bowlers, is
(d) none of these
15. A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. One fruit is picked out from each basket. The probability that the fruits are both apples or both oranges, is
(a) 24/144
(b) 56/144
(c) 68/144
(d) 76/144
16. Given two events A and B. If odds against A are as 2 : 1 and those in favour of A ∪ B are as 3 : 1 , then
(a) 1/2 ≤ P(B) ≤ 3/4
(b) 5/12 ≤ P(B) ≤ 3/4
(c) 1/4 ≤ P(B) ≤ 3/5
(d) none of these
17. If A and B are any two events, then is equal to
(d) none of these
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19. A single letter is selected at random from the word “FAVOURABLE”. The probability that it is a vowel is
(d) None of these
20. The probability that a man can hit a target is 3/4 . He tries 5 times the probability that he will hit the target at most one time is
(d) None of these
21. If p, q are chosen randomly with replacement from the set {1, 2, 3, …………………….,
10}, the probability, that the roots of the equation
22. Three dice are thrown together. Find the probability of getting a total of at least 6.
23. Two numbers x and y are chosen from 0, 1, 2, …………., 10 with replacement. The probability that | x – y | ≤ 5 is
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24. The probability distribution of a random variable X is given as
| x | -5 | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 |
| P(X=x) | p | p | 2p | 3p | 4p | 7p | 8p | 9p | 10p | 11p | 12p |
25. A complete cycle of a traffic light takes 60 seconds. During each cycle the light is green for 25 seconds, yellow for 5 seconds and red for 30 seconds. At a randomly chosen time, the probability that the light will not be green is
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26. In a college, 25% of the boys and 10% of girls offer Mathematics. The girls constitute 60% of the total number of students. If a students is selected at random and is found to be studying Mathematics. The probability that the student is a girl is
(a) 1/6
(b) 3/8
(c) 5/8
(d) 5/6
27. If birth to a male child and birth to a female child are equal probable, then what is the probability that at least one of the three children born to a couple is male?
I. A or B=A ∪ B = {1,2,3}
II. A and B=A ∩ B = {3,5}
III. A but not B = A – B = {2}
IV. Not A = A’ = {1,5,6}
(a) Only I is true
(b) Only II is true
(c) II and III are true
(d) Only IV is true
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29. A coin is tossed three times, consider the following events
A: no head appears
B: exactly one head appears
C: at least two heads appear Then,
(a) A, B and Care mutually exclusive event
(b) A, B and Care exhaustive events
(c) Only (a)
(d) Both (a) and (b)
30. If A and B are any two events associated with random experiment, then by the definition of probability, which of following is true?
(a) Only (i)
(b) Only (ii)
(c) Both (i) and (ii)
(d) None of these
31. Consider the event A = {2,4,6,8} associated with the experiment of drawing a card from a deck of ten cards numbered from 1 to 10. Clearly, the sample space is S = {1,2 3,…10}. Then, which of the following is true?
(iii)
(a) Only (i)
(b) Only (ii)
(c) All are true
(d) (i) and (ii)
32. A bag contains 9 discs. Of which 4 are red, 3 are blue and 2 are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag.
Let the events A, B and C be defined as
A: the disc drawn is red
B: the disc drawn is yellow.
C: the disc drawn is blue.
Then, which of the following is correct?
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(a) (i), (ii) and (iii)
(b) Only (ii)
(c) Only (iv)
(d) (iv) and (v)
33. A committee of two person is selected from two men and two women. The probabilities that the committee will have (i) no man (ii) one man (iii) two men are respectively
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34. For given data which of the following option is true.
(i) P(A) = 0.5, P(B) = 0.7, P(A ⋂ B) = 0.6
(ii) P(A) = 0.5, P(B) = 0.4, P(A ∪ B) = 0.8
(a) (i) is not consistent
(b) (i) is consistent
(c) (ii) is consistent
(d) both (a) and (c)
35. An experiment has four possible outcomes A, B, C and D, that are mutually exclusive. Then, which of the following assignments of probabilities are permissible. (i) P(A)=0.12, P(B) = 0.63, P(C) = 0.45 P(D) = – 0.20
(a) (i) is permissible
(b) (ii) is permissible
(c) Both (i) and (ii) are permissible
(d) Both (i) and (ii) are not permissible
36. If M and N are any two events, the probability that atleast one of the them occurs is K. Here, K refers to
(a) P(M) + P(N) – 2P(M ⋂ N)
(b) P(M) + P(N) – P(M ⋂ N)
(c) P(M) + P(N) + P(M ⋂ N)
(d) P(M) + P(N) + 2P(M ⋂ N)
37. The probability that a leap year will have 53 Fridays or 53 Saturdays, is
38. If any four numbers are selected and they are multiplied, then the probability that the last digit will be 1, 3, 5 or 7, is
(a) 4/625
(b) 18/625
(c) 16/6 25
(d) None of these
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39. If a coin be tossed n times, then probability that the head comes odd times is
(a) 1/2
(d) None of these
40. Fifteen coupons are numbered 1 to 15. Seven coupons are selected at random, one at a time with replacement. The probability that the largest number appearing on a selected coupon be 9, is
(d) None of these
41. The accompanying Venn diagram shows three events, A, B and C and also the probabilities of the various intersections [for instance, P(A ⋂ B) = .07]. Find P(B ⋂ C) and probability of exactly one of the three occurs.
(a) 0.15, 0.15
(b) 0.15, 0.51
(c) 0.15, 0.50
(d) None of these
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42. Three ships A, B and C sail from England to India. If the ratio of their arriving safely are 2 : 5, 3 : 7 and 6 : 11, respectively, then the probability of all the ships for arriving safely is
(a) 18/595
(b) 6/17
(c) 3/10
(d) 2/7
43. The probability that in a random arrangement of the letters of the word ” FAVOURABLE” the two ‘A’ do not come together is
44. Two cards are drawn from a pack of 52 cards. The probability that one card is an ace and other is queen, is
45. A natural number x is chosen at random from 150 natural numbers. The probability that
(d) None of these
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46. In a bag there are 21 balls marked by number 1,2,3, ..21. Two balls are drawn one by one with replacement. What is the probability that from drawn balls first shows odd number and second shows even number.
(d) none of these
48. From X = {1,2,…25}, a number is selected randomly from X and found to be prime. The probability that it is more than 12 is
(d) None of these
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49. Find the probability that the birth days of six different persons will fall in exactly two calender months.
50. A card is drawn from an ordinary pack of 52 cards and a gambler bets that, it is a spade or an ace. What are the odds against his winning this bet?
(a) 9 : 4
(b) 5 : 4
(c) 3 : 8
(d) 2 : 9
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ANSWER KEY
| 1. (d) | 11. (c) | 21. (b) | 31. (c) | 41. (b) |
| 2. (b) | 12. (d) | 22. (d) | 32. (d) | 42. (a) |
| 3. (c) | 13. (b) | 23. (b) | 33. (b) | 43. (d) |
| 4. (a) | 14. (a) | 24. (a) | 34. (d) | 44. (d) |
| 5. (c) | 15. (d) | 25. (d) | 35. (d) | 45. (c) |
| 6. (a) | 16. (b) | 26. (b) | 36. (b) | 46. (b) |
| 7. (c) | 17. (d) | 27. (b) | 37. (b) | 47. (c) |
| 8. (a) | 18. (d) | 28. (c) | 38. (c) | 48. (c) |
| 9. (d) | 19. (d) | 29. (d) | 39. (a) | 49. (b) |
| 10. (a) | 20. (a) | 30. (c) | 40. (c) | 50. (a) |
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