Quantitative Aptitude

Probability

1,860 Questions
All Sample Space Setup 558 Permutation & Combination Counting 288 Multiplication Theorem (AND) 234 Addition Theorem (OR) 151 At Least One Probability 134 Complement Rule (P(Not A)) 130 Drawing Without Replacement 126 Conditional Probability 75 Bayes' Theorem 69 Drawing With Replacement 49 Success and Failure Rates 46

Probability Questions

Multiple choice

A jar contains only green marbles, yellow marbles, and red marbles. If a marble is randomly selected from the jar, what is the probability that the marble will be either yellow or red? (1) The probability that the marble will be red is 0.3. (2) The probability that the marble will be green is 0.4.

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total probability is 1. P(Yellow) + P(Red) + P(Green) = 1. We want P(Yellow or Red) = 1 - P(Green). Statement (2) gives P(Green) = 0.4, so P(Yellow or Red) = 0.6. Statement (1) is insufficient on its own.

Multiple choice

Directions: Compare Quantity I and Quantity II using additional information given above the two quantities, if such information is given, and select one of the following five answer choices. There are 51 playing cards in a box with numbering from 1 to 51. There is no repetition of numbers. Quantity I: Probability of picking up a card whose digits, if interchanged, result in a number which is 9 less than the original number. Quantity II: Probability of picking up a card, the number on which is a multiple of 6 but not that of 9.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or no relation can be established.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: Numbers where interchanging digits reduces value by 9 (e.g., 21-12=9, 32-23=9). Possible numbers: 21, 32, 43, 54(out). Total 3/51. Quantity II: Multiples of 6 (6, 12, 18, 24, 30, 36, 42, 48) excluding multiples of 9 (18, 36). Remaining: 6, 12, 24, 30, 42, 48. Total 6/51. 3/51 < 6/51.

Multiple choice

Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given. Select one of the four answer choices. In a bag, there are 8 red, 5 blue, and 10 green balls. Two balls are drawn, one after the other, with replacement. Quantity A Quantity B If the first ball drawn is red, the probability that both the balls will be of different colours If the first ball drawn is green, the probability that both the balls will be of different colours

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Passage

Directions: Study the given information carefully and answer the following question. 3 groups A, B and C from a school went for a picnic. In each group, there were boys, girls and teachers. In group A, number of boys is 3 more than that of girls. If we have to select one member from this group, then the probability of him being a teacher is 4/11. In group B, number of girls is 50% more than that of boys. If 2 persons are selected from group B at random, then probability of both being teachers is 1/136. Total number of persons in group B is 17. In group C, the ratio of teachers to boys is 1 : 3 and that of teachers to girls is 1 : 4. Total number of persons in this group is 48.

If two persons are selected at random from all groups, then what are the chances of either both being teachers or both being girls?

  1. 661/2850

  2. 47/76

  3. 75/76

  4. 571/2850

  5. 47/5700
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

Passage

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities.

In a bag, there are 5 black, 3 green and 4 red balls. 3 balls are picked at random. Quantity I: The probability that 2 balls are green in colour and 1 ball is red in colour. Quantity II: The probability that all the balls are black in colour.

  1. Quantity I ≤ Quantity II

  2. Quantity I < Quantity II

  3. Quantity I > Quantity II

  4. Quantity I ≥ Quantity II

  5. Quantity I = Quantity II or No relation
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 12. Quantity I: P(2G, 1R) = (3C2 * 4C1) / 12C3 = (3 * 4) / 220 = 12/220. Quantity II: P(3B) = 5C3 / 12C3 = 10 / 220. Since 12/220 > 10/220, I > II.

Multiple choice

Passage

Two quantities that is I and II are given in following questions. Students is expected to solve the quantities and answer them according to given options by comparing their numerical values. निम्नलिखित प्रश्नों में दो मात्राएँ I और II दी गई हैं। छात्रों से अपेक्षा की जाती है कि वे मात्राओं को हल करें और उनके संख्यात्मक मानों की तुलना करके दिए गए विकल्पों के अनुसार उत्तर दें।

Quantity I: What will be the probability of selecting a letter as vowel from the word ‘‘WOMEN’’? Quantity II: Find the probability of selecting 2 Black balls from a bag containing 8 Black balls and 10 green balls? मात्रा I: ‘‘WOMEN’’ शब्द से स्वर के रूप में एक अक्षर का चयन करने की प्रायिकता क्या होगी? मात्रा II: 8 काली गेंदें और 10 हरी गेंदों वाले एक बैग से 2 काली गेंद चुनने की प्रायिकता ज्ञात कीजिये?

  1. Quantity I > Quantity II मात्रा I > मात्रा II

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I < Quantity II मात्रा I < मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relation can’t be established मात्रा I = मात्रा II या सम्बन्ध स्थापित नहीं किया जा सकता है |
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: In 'WOMEN', vowels = O, E (2 out of 5 letters). Probability = 2/5 = 0.4. Quantity II: Selecting 2 black balls from 8 black and 10 green (total 18). Probability = 8C2 / 18C2 = 28 / 153 = 28/153 ≈ 0.183. Since 0.4 > 0.183, Quantity I > Quantity II. Option A is correct.

Multiple choice

Passage

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis.

Quantity I: A bag contains 3 Red balls and 4 blue balls. If one ball is taken out randomly, then find the probability of selecting the ball of blue colour. Quantity II: A bag contains 3 Red and 4 yellow balls. If one ball is taken out randomly, then find the probability of selecting the ball of Red colour.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity I < Quantity II

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: P(blue) = 4/(3+4) = 4/7 ≈ 0.571. Quantity II: P(red) = 3/(3+4) = 3/7 ≈ 0.429. 0.571 > 0.429, so I > II.

Multiple choice

Passage

Study the given information carefully to answer the questions. In an E-commerce company-Liftkart, the growth of the company is driven by the increase in the number of people buying online and the increase in the number of people selling online. In 2020, it was expected that total 100 million people would buy products online in Japan that would be 20% of the total population of Japan and 2% of the total population of Japan would sell products online. If in 2021, the population of Japan was increased by 10% over the previous year together with the total number of people who bought products online was increased by 20% over the previous year and the number of sellers remained constant then in the year 2021 the Industry revenue was $ 50 billion.

In each of the following questions, read the given statement and compare the Quantity I and Quantity II on its basis. (only quantity is to be considered) Quantity I : Probability of obtaining a score of 7 with two fair dice Quantity II : Probability of obtaining two tails and one head when three coins are tossed

  1. Quantity : I > Quantity : II

  2. Quantity : I ≥ Quantity : II

  3. Quantity : I < Quantity : II

  4. Quantity : II ≥ Quantity : I

  5. Quantity I = Quantity II or relation can't be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: P(sum of 7) = favorable/total = 6/36 = 1/6 ≈ 0.167. The pairs summing to 7 are: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1). Quantity II: P(2 tails, 1 head) = 3C2/8 = 3/8 = 0.375. Since 0.375 > 0.167, Quantity II > Quantity I.

Multiple choice

Passage

There are 3 bags containing 3 colored balls - Black, Green and White. Bag 1 contains: 15 black balls. Chances of drawing a white ball is 2/5. The ratio of number of green ball to the number of white ball is 3:4. Bag 2 contains: Number of black balls and number of white balls are equal. Number of green ball is 4/5th of the number of green ball in bag 1. The Chances of black ball is 5/14. Bag 3 contains: Number of Black Balls is (1/3)rd of the total number of black balls in Bag 1 and Bag 2 together. Number of Green ball is half of the number of white ball in bag 1. The probability of drawing a white ball is 3/7.

If one ball is drawn from bag 1 and 1 ball is drawn from bag 3. Find the Chances the these are green ball.

  1. 3/35

  2. 9/245

  3. 11/245

  4. 4/35

  5. 8/35
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Bag 1: White = 2/5, Black = 15. If White = 2/5, then Black+Green = 3/5. Ratio G:W = 3:4. Let G=3x, W=4x. Total = 7x. W/(7x) = 4/7? No, the problem says P(W)=2/5. Let total balls in Bag 1 be N1. W/N1 = 2/5. G/W = 3/4 => G = 3/4 W. B=15. N1 = 15 + W + 3/4 W = 15 + 1.75W. W/(15+1.75W) = 0.4 => W = 6 + 0.7W => 0.3W = 6 => W=20. G=15. Total=50. P(G1) = 15/50 = 3/10. Bag 3: P(W)=3/7. G = 1/2 W(bag1) = 10. B = 1/3(B1+B2). B1=15. B2: B=W, G=4/5*G1=12. P(B)=5/14. B/(B+W+12)=5/14. B/(2B+12)=5/14 => 14B = 10B + 60 => 4B=60 => B=15. B2=15, W2=15. B3 = 1/3(15+15) = 10. Total Bag 3 = 10(B)+10(G)+W3. W3/Total = 3/7. W3/(20+W3) = 3/7 => 7W3 = 60 + 3W3 => 4W3=60 => W3=15. Total Bag 3 = 35. P(G3) = 10/35 = 2/7. P(G1 and G3) = 3/10 * 2/7 = 6/70 = 3/35.

Multiple choice

Passage

There are 3 bags containing 3 colored balls - Black, Green and White. Bag 1 contains: 15 black balls. Chances of drawing a white ball is 2/5. The ratio of number of green ball to the number of white ball is 3:4. Bag 2 contains: Number of black balls and number of white balls are equal. Number of green ball is 4/5th of the number of green ball in bag 1. The Chances of black ball is 5/14. Bag 3 contains: Number of Black Balls is (1/3)rd of the total number of black balls in Bag 1 and Bag 2 together. Number of Green ball is half of the number of white ball in bag 1. The probability of drawing a white ball is 3/7.

N black balls are transferred from bag 1 to bag 3 and (N-2) green balls are transferred from bag 3 to bag 1. One ball is picked from bag 3 and the probability that it is green is 7/37. Find N.

  1. 3

  2. 4

  3. 5

  4. 6

  5. 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice

Passage

The following questions are accompanied by two statements or three statements A, B and C. You have to determine which statement(s) is/are necessary/sufficient to answer the question.

There are x Red, y Blue and 7 Green balls in the bag . What will be the value of yWhen a ball is drawn out of the bag then its probability being Red is 5/18When a ball is drawn out of the bag then its probability being Blue is 3/9

  1. (a)Statement A alone is sufficient

  2. (b)Statement B alone is sufficient

  3. (c)Both statement A and B together are required

  4. (d)Either statement A alone or statement B alone is sufficient

  5. (e)Statement A and B together are not sufficient
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = x + y + 7. P(Red) = x/(x+y+7) = 5/18. P(Blue) = y/(x+y+7) = 3/9 = 1/3 = 6/18. From these, x/(x+y+7) = 5/18 and y/(x+y+7) = 6/18. Thus x+y+7 must be a multiple of 18. Both statements are needed to solve for x and y.

Multiple choice

Passage

(Direction 178-179): Study the given information carefully and answer the questions that follow- A box contains 4 blue, 5 green and 3 red balls.

If three balls are picked at random, what is the probability that either all are red or all are blue?

  1. a) 1/44

  2. b) 1/28

  3. c) 2/55

  4. d) 1/66

  5. e) 3/8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total balls = 4+5+3 = 12. Ways to pick 3 balls = 12C3 = 220. Ways to pick 3 red = 3C3 = 1. Ways to pick 3 blue = 4C3 = 4. Total favorable = 1+4 = 5. Probability = 5/220 = 1/44.

Multiple choice

Passage

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I = Quantity II or the relationship cannot be established from the information given (5) If Quantity I ≤ Quantity II

There are 52 cards in a box and the cards are numbered from 1 to 52. Quantity I: Probability of picking a card, whose digits if interchanged, result in a number which is 45 more than the number card picked. Quantity II: Probability of picking a card, the number printed on which is a multiple of 4, but not that of 8.

  1. (1)

  2. (2)

  3. (3)

  4. (4)

  5. (5)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: Numbers xy such that (10y+x) - (10x+y) = 45 => 9(y-x) = 45 => y-x = 5. Pairs: (1,6), (2,7), (3,8), (4,9). Total 4 cards. P(I) = 4/52 = 1/13. Quantity II: Multiples of 4 but not 8 are 4, 12, 20, 28, 36, 44, 52. Total 7 cards. P(II) = 7/52. Since 1/13 = 4/52 < 7/52, Quantity I < Quantity II.

Multiple choice

Passage

Directions: Read the following information carefully and answer the question that follow: A piggy-bank contains total 18 coins of Re 1, 50 paise and 25 paise. The difference between Re 1 and 50 paise coins is same as difference between 50 paise and 25 paise coins.

If probability of selecting one 25 paise is more than 0.5, then number of Re. 1 coins can be

  1. 1

  2. 2

  3. 3

  4. Both 1 and 2

  5. 1, 2 and 3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let coins be x, y, z for 1, 0.5, 0.25. x+y+z=18. x-y = y-z => x+z = 2y. 3y=18 => y=6. x+z=12. Probability of 25p (z) > 0.5 means z/18 > 0.5, so z > 9. Since x+z=12 and z > 9, possible values for z are 10, 11, 12. Then x = 12-z, so x can be 2, 1, 0. Since there must be coins of each type, x can be 1 or 2.

Multiple choice

Passage

Directions: Read the following information carefully and answer the question that follow: A piggy-bank contains total 18 coins of Re 1, 50 paise and 25 paise. The difference between Re 1 and 50 paise coins is same as difference between 50 paise and 25 paise coins.

If probability of selecting one 50 paise is double the probability of selecting Re. 1 coin then difference between Re 1 and 25 paise coins can be

  1. 6

  2. 8

  3. 9

  4. 10

  5. 11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let x, y, z be the number of Re 1, 50p, and 25p coins. x+y+z=18. x-y = y-z implies x+z=2y. Substituting into x+y+z=18 gives 3y=18, so y=6. x+z=12. Probability P(50p) = 2*P(Re 1) implies y/18 = 2*(x/18), so y=2x. Since y=6, x=3. Then z=9. Difference between Re 1 and 25p is |3-9| = 6.