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

There is a basket full of hats. Three of them are red and two of them are blue. There are 3 men; Timothy, Imran and Jatin. Jatin is colour blind for both these colours. They each take a hat out of the basket and put it on their heads without seeing the hat they selected or the hats the other men selected. The men arrange themselves in such a manner so that Timothy can see Imran and Jatin's hats, Imran can see Jatin's hat and Jatin can't see anyone's hat. However, they can hear each other. Also, they do know the initial number of red and blue hats. Timothy is asked what colour his hat is and he says he doesn't know. Imran is asked the same question, and he also doesn't know. Finally, Jatin is asked the question, and he does know. What colour is his hat?

  1. Red

  2. Blue

  3. Red or blue as Jatin will see it

  4. Black, because colour blind people see dark colours as black

  5. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The hat is red. If Timothy doesn't know his hat colour, then the other two men's hats cannot be both blue otherwise he would know his hat is red. When Imran doesn't know his hat colour either, that means Jatin's hat could not be blue otherwise Imran would have to know his hat was red to fulfill the information discovered through Timothy's answer.

Multiple choice

Six balls are drawn at random from a bag containing six white, five green and four black balls. The probability that exactly 3 of them are white is

  1. 16/143

  2. 48/143

  3. 12/143

  4. 32/143

  5. 4/1001
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

It is the correct answer. Solution- Total no of balls = 15No of ways of drawing 6 balls from 15 balls randomly=15C6 No of ways of drawing 3 white balls from 6 white balls = 6C3 No of ways of drawing other 3 balls from remaining 9 balls = 9C3 Required probability=(6C3 * 9C3) / 15C6 = 48/143

Multiple choice

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red is

  1. 2/91

  2. 89/91

  3. 4/91

  4. 1/3

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

Probability of all the three balls being red  = 5C3/15C3                                                                              = 10/455                                                                              = 2/91 Hence, this option is correct.

Multiple choice

Two dice are thrown simultaneously. The probability of obtaining a total score of eight is

  1. 5/36

  2. 1/6

  3. 1/9

  4. 1/12

  5. 5/12
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When two dice are thrown then there are 6 * 6 exhaustive cases. Therefore, n = 36.

Let A denote the event total score of 8 when 2 dice are thrown. Then A = {(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)}

Thus, there are 5 favourable cases.

Therefore, m = 5

By definition P(A) = m/n = 5/36.

It is the correct answer.

Multiple choice

A box contains 6 blue and 5 pink balls. Two balls are picked randomly one after the other from the box, without replacement. What is the probability that both balls are pink?

  1. 2/11

  2. 1/11

  3. 5/11

  4. 6/11

  5. 2/10
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probability of drawing a pink ball is 5/11. If the ball is not replaced, then the box will have one less pink ball, so the probability of drawing a pink ball in the next chance is 4/10. Hence, the probability of drawing 2 pink balls = 5/11 * 4/10 = 2/11. Hence, it is the correct answer.

Multiple choice

What is the probability of getting a prime number which is greater than or equal to five, when rolling a die?

  1. 2/6

  2. 1/6

  3. 1/2

  4. 4/6

  5. 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a die, there are only six numbers, i.e. 1, 2, 3, 4, 5, 6. A prime number is a number which can be divided by itself and 1. Now, find a prime number that is greater than or equal to 5, which is only number five. Hence, the probability will be 1/6. Hence, it is the correct answer.

Multiple choice

Which of the following are the various events of getting the sum of numbers as seven, when rolling a pair of dice?

  1. {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2),(6, 0)}

  2. {(1, 6),(2, 5),(3, 4),(5, 2),(6, 1)}

  3. {(1, 6),(2, 5),(3, 4),(3, 3),(5, 2),(6, 1)}

  4. {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2),(6, 1)}

  5. {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2)}
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

It is the correct answer. In a die, there are only six numbers – 1, 2, 3, 4, 5, and 6. Various events of getting sum of dice as seven when rolling a pair of dice will be as follows: {(1, 6),(2, 5),(3, 4),(4, 3),(5, 2),(6, 1)}

Multiple choice

Two cards are drawn in succession from a pack of 52 cards. The first card should be a Queen and the second should be a King. What is the probability when the first card is replaced?

  1. 1/52

  2. 1/13

  3. 2/50

  4. 1/169

  5. 2/52
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Probability of drawing a Queen is 4/52 = 1/13. Since the card is replaced, the pack will again have 52 cards. So, the probability of drawing a King is 4/52 = 1/13. Both events are independent, hence the probability of drawing both cards in succession is 1/13 * 1/13 = 1/169.