Mathematics

Probability

303 Questions

Probability measures the likelihood of an event occurring, such as rolling a specific number on a die or drawing a colored ball. Questions cover simple events, mutually exclusive outcomes, and dice or coin combinations. This topic is consistently asked in mathematics and reasoning sections of competitive exams.

dice probabilitycoin toss eventsdrawing balls probabilitiesplaying card problemsmutually exclusive events

Probability Questions

Multiple choice

What is the probability of getting a sum of 7 when rolling 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

When rolling two dice, there are 36 possible outcomes. The outcomes that result in a sum of 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

A coin is tossed three times. What is the probability of getting exactly two heads?

  1. 1/4

  2. 1/8

  3. 3/8

  4. 1/2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

There are 8 possible outcomes when a coin is tossed three times: HHH, HHT, HTH, THH, THT, TTH, HTT, TTT. There are 3 outcomes with exactly two heads: HHT, HTH, THH. Therefore, the probability of getting exactly two heads is 3/8.

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 20 green balls. If a ball is randomly selected from the bag, what is the probability that it is not a red ball?

  1. 1/2

  2. 2/5

  3. 3/5

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

There are a total of 10 + 15 + 20 = 45 balls in the bag. The probability of selecting a red ball is 10/45. Therefore, the probability of selecting a ball that is not red is 1 - 10/45 = 4/5.

Multiple choice

Which of the following is a mathematical concept that is used in the game of Ludo?

  1. Probability

  2. Statistics

  3. Calculus

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

Probability is a mathematical concept that is used to calculate the likelihood of an event occurring. In the game of Ludo, probability is used to determine the chances of a player rolling a particular number on the dice.

Multiple choice

Which of the following is a mathematical concept that is used in the game of Go?

  1. Probability

  2. Statistics

  3. Calculus

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

Calculus is a mathematical concept that is used to study the rate of change. In the game of Go, calculus is used to determine the best move to make in a given situation.

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 20 green balls. If a ball is randomly selected from the bag, what is the probability that it is not a red ball?

  1. 1/2

  2. 2/5

  3. 3/5

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

The total number of balls in the bag is 10 + 15 + 20 = 45. The number of balls that are not red is 45 - 10 = 35. Therefore, the probability of selecting a ball that is not red is 35/45 = 3/5.

Multiple choice

A bag contains 15 red balls, 20 blue balls, and 25 green balls. If a ball is randomly selected from the bag, what is the probability that it is a blue ball?

  1. 1/2

  2. 2/5

  3. 3/5

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

The total number of balls in the bag is 15 + 20 + 25 = 60. The number of blue balls in the bag is 20. Therefore, the probability of selecting a blue ball is 20/60 = 2/5.

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 if at least one ball of each color is to be included?

  1. 168

  2. 120

  3. 96

  4. 80
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

First, select 1 red ball from 6 red balls, which can be done in 6 ways. Then, select 1 blue ball from 4 blue balls, which can be done in 4 ways. Finally, select 1 green ball from 2 green balls, which can be done in 2 ways. Therefore, the total number of ways to select 3 balls, one of each color, is 6 * 4 * 2 = 48. Since there are 3 different colors, there are 3 different ways to choose which color ball to select first. Therefore, the total number of ways to select 3 balls, at least one of each color, is 3 * 48 = 144.

Multiple choice

A bag contains 6 red balls, 4 blue balls, and 2 green balls. In how many ways can 4 balls be selected from the bag if the selection must include at least 1 red ball and at least 1 blue ball?

  1. 240

  2. 120

  3. 60

  4. 30
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First, select 1 red ball from 6 red balls, which can be done in 6 ways. Then, select 1 blue ball from 4 blue balls, which can be done in 4 ways. Now, we have 2 balls left to select, and we can choose either 2 green balls or 1 green ball and 1 red ball or 1 green ball and 1 blue ball. The number of ways to select 2 green balls from 2 green balls is 2C2 = 1. The number of ways to select 1 green ball and 1 red ball from 2 green balls and 5 red balls is 2C1 * 5C1 = 10. The number of ways to select 1 green ball and 1 blue ball from 2 green balls and 3 blue balls is 2C1 * 3C1 = 6. Therefore, the total number of ways to select 4 balls, including at least 1 red ball and at least 1 blue ball, is 6 * 4 * (1 + 10 + 6) = 240.

Multiple choice

A bag contains 10 red balls, 15 blue balls, and 20 green balls. In how many ways can 6 marbles be selected from the bag if there must be twice as many red marbles as blue marbles and three times as many green marbles as blue marbles?

  1. 140

  2. 70

  3. 35

  4. 17
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let x be the number of blue marbles to be selected. Then, the number of red marbles to be selected is 2x, and the number of green marbles to be selected is 3x. Since we are selecting a total of 6 marbles, we have x + 2x + 3x = 6, which gives x = 1. Therefore, we need to select 1 blue marble, 2 red marbles, and 3 green marbles. The number of ways to select 1 blue marble from 15 blue marbles is 15C1 = 15. The number of ways to select 2 red marbles from 10 red marbles is 10C2 = 45. The number of ways to select 3 green marbles from 20 green marbles is 20C3 = 1140. Therefore, the total number of ways to select 6 marbles, with twice as many red marbles as blue marbles and three times as many green marbles as blue marbles, is 15 * 45 * 1140 = 777000.

Multiple choice

A bag contains 8 red balls, 6 blue balls, and 4 green balls. In how many ways can 6 balls be selected from the bag if there must be an equal number of red, blue, and green balls?

  1. 56

  2. 28

  3. 14

  4. 7
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since there must be an equal number of red, blue, and green balls, we need to select 2 balls from each color. The number of ways to select 2 red balls from 8 red balls is 8C2 = 28. The number of ways to select 2 blue balls from 6 blue balls is 6C2 = 15. The number of ways to select 2 green balls from 4 green balls is 4C2 = 6. Therefore, the total number of ways to select 6 balls, 2 of each color, is 28 * 15 * 6 = 2520.

Multiple choice

What is the probability of getting a head when flipping a 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

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

Multiple choice

What is the probability of getting a head when flipping a 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

When flipping 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 rolling 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

When rolling two dice, there are 36 possible outcomes. 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

A bag contains 5 red balls, 3 blue balls, and 2 green balls. If you randomly select a ball from the bag, what is the probability of selecting a blue ball?

  1. 1/5

  2. 1/4

  3. 3/10

  4. 1/2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The probability of selecting a blue ball is the ratio of the number of blue balls to the total number of balls in the bag. There are 3 blue balls and a total of 5 + 3 + 2 = 10 balls in the bag. Therefore, the probability of selecting a blue ball is 3/10.