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 contains 7 red pens and 5 blue pens and another bag contains 4 red pens and 8 blue pens. One bag is chosen randomly and one pen is drawn from it. If the pen drawn is red, then what is the probability that it is from the first bag?

  1. 7/22

  2. 11/18

  3. 7/11

  4. 17/24

  5. 8/17
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Using Bayes' Theorem: P(Bag1|Red) = P(Red|Bag1)P(Bag1) / (P(Red|Bag1)P(Bag1) + P(Red|Bag2)P(Bag2)). P(Red|Bag1) = 7/12, P(Red|Bag2) = 4/12. P(Bag1) = P(Bag2) = 1/2. Calculation: (7/12 * 1/2) / ((7/12 * 1/2) + (4/12 * 1/2)) = 7/11.

Multiple choice

Consider an experiment of tossing two fair dice, one black and one red. What is the probability that the number on the black die divides the number on red die?

  1. 22/36

  2. 12/36

  3. 14/36

  4. 6/36
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The total outcomes are 6 * 6 = 36. Favorable outcomes (black die d, red die r such that d divides r): (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,2), (2,4), (2,6), (3,3), (3,6), (4,4), (5,5), (6,6). Counting these gives 14 pairs.

Multiple choice

There are three cards in a box. Both sides of one card are black, both sides of second card are red, and the third card has one black side and one red side. We pick a card at random and observe only one side. What is the probability that the opposite side is of the same colour as that of the one side we observed?

  1. 3/4

  2. 2/3

  3. 1/2

  4. 1/3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are 6 sides total: 2 black (card 1), 2 red (card 2), 1 black and 1 red (card 3). If you observe a black side, it could be one of the 2 sides of card 1 or the 1 black side of card 3 (3 possibilities). In 2 of those cases, the other side is black. Probability = 2/3.

Multiple choice

A card is drawn from a pack of well-shuffled cards. What is the probability of getting a card bearing a prime number?

  1. 5 13

  2. 1 13

  3. 5 52

  4. 4 13
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A standard deck has 52 cards. Prime numbers between 1 and 13 are 2, 3, 5, 7, 11, 13 (there are 6). However, in a deck, the cards are Ace (1), 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack (11), Queen (12), King (13). Prime values are 2, 3, 5, 7, 11, 13. There are 4 of each, so 6 * 4 = 24 cards. 24/52 = 6/13. The provided answer 4/13 suggests only 2, 3, 5, 7 are counted (excluding 11, 13). Given the options, 4/13 is the intended answer.

Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: Sam has x flavors of candies with which to make goody bags for Frank's birthday party. Sam tosses out y flavors, because he doesn't like them. How many different 10-flavor bags can Sam make from the remaining flavors? (It doesn't matter how many candies are in the bag, only how many flavors). (1) If Sam had thrown away two more flavors of candy, he could have made exactly 3,003 different 10-flavor bags. (2) x = y + 17

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

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

  3. Both statements (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both statements independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement 1: (x-y-2)C10 = 3003. Since 15C10 = 3003, x-y-2 = 15, so x-y = 17. Statement 2: x-y = 17. Both statements provide the same information independently.

Multiple choice

Directions: The question given below is followed by three statements numbered I, II and III. Read all the statements carefully and decide which of them is/are sufficient to answer the given question. Choose the correct alternative accordingly. What is the probability of picking 1 red and 1 white ball from a bag containing balls of three colours without replacement? I. The bag contains red, white and blue balls in the ratio 3 : 5 : 7. II. The bag contains 75 balls. III. The number of red balls in the bag is 40% less than number of white balls.

  1. Only I

  2. Only II and III

  3. Only I and III

  4. Only I and II

  5. Even I, II and III together are not sufficient.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the probability of picking 1 red and 1 white ball, we need the total number of balls and the count of each color. Statement I gives the ratio (3:5:7), and Statement II gives the total (75). With these, we can find the exact number of red, white, and blue balls, which is sufficient.