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 5 red balls, 3 blue balls, and 2 green balls. What is the probability of randomly selecting a blue ball?

  1. 5/10

  2. 3/10

  3. 2/10

  4. 1/10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of selecting a blue ball is the number of blue balls divided by the total number of balls. So, the probability is 3 / (5 + 3 + 2) = 3/10.

Multiple choice

A bag contains 4 red balls, 3 blue balls, and 2 green balls. If two balls are randomly selected without replacement, what is the probability that the first ball is red and the second ball is blue?

  1. 3/14

  2. 6/35

  3. 2/21

  4. 1/10
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The probability of selecting a red ball on the first draw is 4/9. After the first draw, there are 3 red balls, 3 blue balls, and 2 green balls remaining. The probability of selecting a blue ball on the second draw is 3/8. Therefore, the probability of selecting a red ball on the first draw and a blue ball on the second draw is (4/9) * (3/8) = 3/35.

Multiple choice

A fair six-sided die is rolled twice. What is the probability of getting a sum of 7?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 36 possible outcomes when rolling a fair six-sided die twice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So, the probability of getting a sum of 7 is 6/36 = 1/6.

Multiple choice

A box contains 6 red balls, 4 blue balls, and 2 green balls. In how many ways can 3 balls be selected from the box?

  1. 80

  2. 120

  3. 90

  4. 100
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is a combination problem. We have 12 total balls, and we need to choose 3 of them. Therefore, the total number of ways is 12 * 11 * 10 / 3! = 120.

Multiple choice

A bag contains 10 red marbles, 15 blue marbles, and 20 green marbles. In how many ways can 5 marbles be selected from the bag if at least one marble of each color must be included?

  1. 1,260

  2. 1,008

  3. 1,120

  4. 960
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

We can first select 1 red marble in 10 ways, 1 blue marble in 15 ways, and 1 green marble in 20 ways. Then, we can select the remaining 2 marbles in 9 * 8 / 2! = 36 ways. Therefore, the total number of ways is 10 * 15 * 20 * 36 = 1,120.

Multiple choice

What is the probability of getting a head when you flip a coin?

  1. 1/2

  2. 1/4

  3. 1/3

  4. 1/6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When you flip a coin, there are two possible outcomes: heads or tails. Since each outcome is equally likely, the probability of getting a head is 1/2.

Multiple choice

What is the probability of getting a sum of 7 when you roll two dice?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 36 possible outcomes when you roll two dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). So, the probability of getting a sum of 7 is 6/36 = 1/6.

Multiple choice

What is the probability of obtaining a head when flipping a fair coin?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Since a fair coin has two equally likely outcomes (head or tail), the probability of obtaining a head is 1/2.

Multiple choice

What is the probability of getting two heads when flipping two coins?

  1. 1/4

  2. 1/2

  3. 3/4

  4. 1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When flipping two coins, there are four possible outcomes: HH, HT, TH, and TT. Since each outcome is equally likely, the probability of getting two heads is (1/4).

Multiple choice

In a fair coin toss, what is the probability of getting heads?

  1. 1/2

  2. 1/4

  3. 1/3

  4. 1/6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a fair coin toss, there are two equally likely outcomes: heads or tails. Therefore, the probability of getting heads is 1/2.

Multiple choice

What is the probability of getting at least one head in two coin tosses?

  1. 1/2

  2. 1/4

  3. 3/4

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

The probability of getting at least one head in two coin tosses is the complement of the probability of getting no heads. The probability of getting no heads is (1/2)^2 = 1/4. Therefore, the probability of getting at least one head is 1 - 1/4 = 3/4.

Multiple choice

What is the probability of getting exactly two heads in three coin tosses?

  1. 1/2

  2. 1/4

  3. 3/8

  4. 1/8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of getting exactly two heads in three coin tosses is given by the binomial distribution with n = 3 and p = 1/2. The probability of getting exactly k heads in n coin tosses is given by P(X = k) = (n choose k)p^k(1-p)^(n-k). In this case, P(X = 2) = (3 choose 2)(1/2)^2(1/2)^1 = 3/8.

Multiple choice

What is the probability of getting a sum of 7 in a roll of two fair dice?

  1. 1/6

  2. 1/12

  3. 1/18

  4. 1/24
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are 36 possible outcomes when rolling two fair dice. The outcomes that sum to 7 are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). Therefore, the probability of getting a sum of 7 is 6/36 = 1/6.

Multiple choice

What is the probability of getting a head when a fair coin is tossed?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

When a fair coin is tossed, there are two possible outcomes: head or tail. Since each outcome is equally likely, the probability of getting a head is 1/2.

Multiple choice

A box contains 12 red balls, 8 blue balls, and 6 green balls. If a ball is randomly selected from the box, what is the probability of selecting a red ball?

  1. 1/2

  2. 1/3

  3. 2/5

  4. 3/8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To find the probability of selecting a red ball, we divide the number of red balls by the total number of balls: 12 red balls / (12 red balls + 8 blue balls + 6 green balls) = 12/26 = 1/2.