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

Find the correct relationship between given quantities. Quantity I- A bag contains 3 green, 2 yellow and 3 purple balls. Two balls are drawn at random, what is the probability that no ball is purple. Quantity II- A bag contain 4 red balls and 6 yellow balls.If three balls are picked randomly then what is the probability that they are of the same color.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: P(no purple) = C(5,2)/C(8,2) = 10/28 = 5/14 ≈ 0.357. Quantity II: P(all same color) = P(all red) + P(all yellow) = C(4,3)/C(10,3) + C(6,3)/C(10,3) = 4/120 + 20/120 = 24/120 = 1/5 = 0.2. Since 0.357 > 0.2, Quantity I > Quantity II.

Multiple choice

Answer the following questions based on statement given below- Two dice are rolled simultaneously. Find the probability of getting at least one 5.
  1. $\(\frac{13}{36}\)$
  2. $\(\frac{11}{36}\)$
  3. $\(\frac{10}{33}\)$
  4. $\(\frac{11}{35}\)$
  5. $\(\frac{12}{35}\)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For two dice, total outcomes = 36. Getting at least one 5 means either exactly one 5 or two 5s. Probability of at least one 5 = 1 - probability of no 5s = 1 - (5/6 × 5/6) = 1 - 25/36 = 11/36. Alternatively, count favorable outcomes: (5,1-6) and (1-6,5) gives 11 outcomes out of 36.

Multiple choice

From a pack of 52 playing cards jacks, queens, kings and aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is a picture card. 52 प्लेइंग कार्ड्स के पैक से लाल रंग के जैक, क्वीन, किंग और इक्के निकाल लिए जाते हैं। शेष में से, एक कार्ड यादृच्छिक रूप से चुना जाता है । क्या प्रायिकता है कि खींचा गया कार्ड एक चित्र कार्ड है।

  1. 3/25

  2. 5/22

  3. 3/22

  4. 1/22
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After removing 8 red face cards and aces from the 52-card deck, 44 cards remain. The remaining picture cards are only the 6 black face cards (J, Q, K of clubs and spades). Probability = 6/44 = 3/22.

Multiple choice

Find the probability of getting a numbered card when a card is drawn from the pack of 52 cards. 52 कार्डों के पैक से एक कार्ड निकाले जाने पर एक संख्या वाले कार्ड को प्राप्त करने की प्रायिकता ज्ञात कीजिये ।

  1. 7/13

  2. 8/13

  3. 9/13

  4. 11/13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A standard deck has 52 cards with 4 suits. Each suit has 9 numbered cards (2-10), giving 36 numbered cards total. Probability = 36/52 = 9/13 after simplification by dividing numerator and denominator by 4.

Multiple choice

What is the probability of getting a 2 or a 5 when a die is rolled?
  1. $\(\frac{1}{3}\)$
  2. $\(\frac{1}{4}\)$
  3. $\(\frac{1}{6}\)$
  4. $\(\frac{1}{2}\)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A standard die has 6 faces numbered 1-6. The favorable outcomes are getting either 2 OR 5, which are 2 distinct outcomes. Probability = Favorable outcomes / Total outcomes = 2/6 = 1/3. Option A (1/3) is correct.

Multiple choice

A bag contains 8 black and 7 white balls. One ball is drawn at random. What is the probability that the ball drawn is white?
  1. $\frac{8}{15}$
  2. $\frac{8}{7}$
  3. $\frac{7}{15}$
  4. $\frac{1}{7}$

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Total balls = 8 black + 7 white = 15. Probability of drawing white = favorable outcomes / total outcomes = 7/15. Option C is correct. Option A (8/15) is the probability of drawing black. Options B and D are incorrect as they don't represent valid probability fractions for this scenario.

Multiple choice

A bag contains 5 Red , 3 Blue and 4 Black balls. 3 balls are drawn randomly then what is the probability getting exactly one balls is red?
  1. $2/5$
  2. $1/132$
  3. $2/33$
  4. $21/44$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total balls = 5R + 3B + 4Black = 12. We need exactly 1 red in 3 draws. Number of ways to choose 1 red from 5 and 2 non-red from 7 = C(5,1) × C(7,2) = 5 × 21 = 105. Total ways to choose any 3 balls from 12 = C(12,3) = 220. Probability = 105/220 = 21/44 after dividing by 5. The calculation 105/220 simplifies to 21/44.

Multiple choice

A bag contains 9 Red and 7 Pink balls. There is another bag which contains 8 Red and 11 Pink balls. One ball is to be drawn from either of the two bags. What is the probability of drawing a Pink ball?

  1. 309/608

  2. 308/609

  3. 208/609

  4. 209/608

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Total balls = 9+7+8+11 = 35. Pink balls = 7+11 = 18. Probability = 18/35. However, the question says one ball is drawn from EITHER bag, meaning we first choose a bag (probability 1/2 each), then draw a ball. If we choose bag 1, P(pink) = 7/16. If we choose bag 2, P(pink) = 11/19. Total P = (1/2)(7/16) + (1/2)(11/19) = 7/32 + 11/38 = (7×19 + 11×16)/(32×19) = (133 + 176)/608 = 309/608. This matches option A.

Multiple choice

In a bag which contains 40 balls, there are 18 red balls and some green and blue balls. If two balls are picked up from the bag without replacement, then the probability of the first ball being red and second being green is 3/26. Find the number of blue balls in the bag.

  1. 12

  2. 10

  3. 18

  4. None of these

  5. Can’t be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let green balls = g. Probability first red then green = (18/40) * (g/39) = 3g/260. Given this equals 3/26, so g = 10. Total balls = 40, so blue = 40 - 18 - 10 = 12. Answer A is correct.

Multiple choice

From a bag which contains 4 black balls, 3 green balls and 5 yellow balls, what is the probability of selecting 3 balls of different colors?

  1. 6/11

  2. 3/11

  3. 1/2

  4. 4/11
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total balls = 4+3+5 = 12. To get 3 balls of different colors (1 black, 1 green, 1 yellow), calculate: (4/12)×(3/11)×(5/10) = 60/1320 = 1/22. Since the 3 colors can be arranged in 3! = 6 ways, total probability = 6 × (1/22) = 6/22 = 3/11. This considers all possible orders of drawing one ball of each color.

Multiple choice

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. 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?

  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 relation can’t be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: In 'WOMEN', vowels are O and E (2 out of 5), probability = 2/5 = 0.4. Quantity II: Selecting 2 Black balls from 8 Black and 10 Green (total 18). Probability = C(8,2) / C(18,2) = 28/153 ≈ 0.183. Since 0.4 > 0.183, Quantity I > Quantity II.