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 bag has 15 red, green and blue balls. Number of each balls is different in the bag. Difference between red ball and green ball is same as difference between green ball and blue ball. Probability of selecting one blue ball from the bag is greater than 0.2, then number of blue balls in the bag can be (A) 3(B) 4(C) 5(D) 7(E) 9

  1. (a) Only B, C, D and E

  2. (b) Only B, D, E

  3. (c) All A, B, C, D and E

  4. (d) Only C, D, E

  5. (e) Only A, B, D, E
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

A box contains x red balls, y yellow balls and 5 black balls and the number of red balls is 50% more than yellow balls in that box. If the probability of drawn a yellow balls in the box is 4/15, then find the total number of balls in the box?

  1. 30

  2. 15

  3. 21

  4. 45

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

Red = 1.5 * Yellow. Let Yellow = y, Red = 1.5y, Black = 5. Total = 2.5y + 5. P(Yellow) = y / (2.5y + 5) = 4/15. 15y = 10y + 20, so 5y = 20, y = 4. Red = 6. Total = 4 + 6 + 5 = 15.

Multiple choice

A box contains 4 Red balls, 3 white balls, 5 orange balls and 6 blue balls. Quantity I: If two balls are drawn at random, then find the probability that both the balls are either orange or blue? Quantity II: If four balls are drawn at random, then find the probability that all the balls are different in colour?

  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

Total balls = 4+3+5+6 = 18. Quantity I: P(2 orange or 2 blue) = (5C2 + 6C2) / 18C2 = (10 + 15) / 153 = 25/153 approx 0.163. Quantity II: P(4 different) = (4C1 * 3C1 * 5C1 * 6C1) / 18C4 = (4*3*5*6) / 3060 = 360 / 3060 approx 0.117. Quantity I > Quantity II.

Multiple choice

. In a bag there are 3 magenta balls, 5 green balls and 7 blue balls . 2 balls are drawn one by one without replacement. If the first ball comes out to be of magenta colour, then 8 more magenta coloured balls are added to bag. Find the probability that both the balls drawn are of magenta colour.

  1. 1/11

  2. 2/11

  3. 3/23

  4. 4/23

  5. 6/11
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Initial: 3M, 5G, 7B (Total 15). First ball is M: P(M1) = 3/15. Remaining: 2M, 5G, 7B. Add 8M: 10M, 5G, 7B (Total 22). P(M2|M1) = 10/22 = 5/11. P(M1 and M2) = (3/15) * (5/11) = (1/5) * (5/11) = 1/11.

Multiple choice

Two cards are drawn at random from a standard deck of 52 playing cards without replacement. What is the probability that the first card is a Queen and the second card is a King? (a) 1/169 (b) 4/663 (c) 8/663 (d) 1/221 (e) 4/221

  1. C

  2. E

  3. D

  4. B

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

The probability of drawing a Queen first is 4/52, followed by a King with probability 4/51. Thus the required probability is (4/52)(4/51) = 4/663, which corresponds to choice (b).