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 pot contains 5 white and 3 red balls while another pot contains 4 white and 6 red balls. One pot is chosen at random and a ball is drawn from it. If the ball is white, what is the probability that it is from the first pot?

  1. 5/16

  2. 41/80

  3. 25/41

  4. 1/5

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

P(Pot1) = 1/2, P(White|Pot1) = 5/8. P(Pot2) = 1/2, P(White|Pot2) = 4/10 = 2/5. P(White) = (1/2 * 5/8) + (1/2 * 2/5) = 5/16 + 1/5 = (25+16)/80 = 41/80. P(Pot1|White) = (P(White|Pot1) * P(Pot1)) / P(White) = (5/16) / (41/80) = (5/16) * (80/41) = 25/41.

Multiple choice

Andrew has a certain number of soccer balls with him. He wants to take two of the soccer balls for Match-1 on Monday and three of the soccer balls for Match-2 on Tuesday. There are exactly 15 ways in which he can select the soccer balls for Match-1, and all soccer balls can be used for both the matches. In how many different ways can Andrew select the soccer balls for Match-2?

  1. 20

  2. 15

  3. 10

  4. 9

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

Let n be the number of soccer balls. Selecting 2 balls in 15 ways means nC2 = 15. n(n-1)/2 = 15, so n(n-1) = 30, n = 6. Selecting 3 balls for the second match is 6C3 = (6*5*4)/(3*2*1) = 20.

Multiple choice

Given below are two statements: Statement I: A coin is tossed three times. The probability of getting exactly two heads is 3 8 . Statement II: In tossing of 10 coins, the probability of getting exactly 5 heads is 63 256 . In light of the above statements, choose the correct answer from the options given below.

  1. Both Statement I and Statement II are true.

  2. Both Statement I and Statement II are false.

  3. Statement is true, but Statement II is false.

  4. Statement I is false, but Statement II is true.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For three tosses, exactly two heads can occur in 3 outcomes out of 8, giving 3/8. For ten tosses, exactly five heads has probability 252/1024 = 63/256, so both statements are true.

Multiple choice

Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 8, what is the probability that one of the two cards drawn is numbered 5?

  1. 1/6

  2. 1/5

  3. 1/3

  4. 2/5

  5. 2/3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The total outcomes for two draws are 6 * 6 = 36. The pairs that sum to 8 are (2,6), (3,5), (4,4), (5,3), (6,2). There are 5 such outcomes. Among these, the outcomes containing a 5 are (3,5) and (5,3). The probability is 2/5.

Multiple choice

A bag contains 25 marbles, out of which some are red and some are blue. After taking one blue marble out, the probability of selecting a red marble is 3 8 . What is the probability of selecting a blue marble before taking the blue marble out?

  1. 5 8

  2. 15 27

  3. 16 24

  4. 16 25

  5. 14 30
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let R be red and B be blue. Total = 25. After removing one blue, total = 24. P(Red) = R/24 = 3/8, so R = 9. Blue marbles = 25 - 9 = 16. Probability of blue before removal = 16/25.

Multiple choice

Directions: An urn has 6 red marbles, 8 green marbles and 11 blue marbles. Three marbles are drawn. What is the probability that at least one of them is green?

  1. 34/115

  2. 81/115

  3. 14/575

  4. 91/115

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

Total marbles = 6+8+11 = 25. Probability of no green = (17/25) * (16/24) * (15/23) = (17/25) * (2/3) * (15/23) = (17 * 2 * 5) / (25 * 23) = 170 / 575 = 34/115. Probability of at least one green = 1 - 34/115 = 81/115.

Multiple choice

Bag A contains 2 white, 1 black and 3 red balls and bas B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is 6/11 then n is equal to _______.

  1. 13

  2. 6

  3. 4

  4. 3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of drawing one red and one black ball from Bag A is 1/5. For Bag B, applying the given conditional probability requires the corresponding likelihood to be 1/6, which gives C(n + 5, 2) = 36. Hence n + 5 = 9 and n = 4.

Multiple choice

Directions: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given, and select one of the following four answer choices: Quantity A Quantity B Number of ways to select 2 balls at random from 30 balls Number of ways to select 2 balls at random, one red and one white, when there are 15 red and 15 white balls

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity A: Choosing 2 from 30 is 30C2 = (30*29)/2 = 435. Quantity B: Choosing 1 red from 15 and 1 white from 15 is 15 * 15 = 225. Since 435 > 225, A is greater.