Mathematics

Probability

337 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 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 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

A fair coin has two possible outcomes: head and tail. 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 fair dice?

  1. 1/6

  2. 1/5

  3. 1/4

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

There are 36 possible outcomes when rolling two 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

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 a red ball?

  1. 1/5

  2. 2/5

  3. 3/5

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

There are a total of 10 + 15 + 20 = 45 balls in the bag. The probability of selecting a red ball is the number of red balls divided by the total number of balls, which is 10 / 45 = 1/5.

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.

Multiple choice

A box contains 15 red balls, 10 blue balls, and 5 green balls. If a ball is randomly selected from the box, what is the probability of selecting a blue ball?

  1. 1/3

  2. 1/4

  3. 1/5

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

To find the probability of selecting a blue ball, we divide the number of blue balls by the total number of balls: 10 blue balls / (15 red balls + 10 blue balls + 5 green balls) = 10/30 = 1/3.

Multiple choice

What is the probability of getting a head when flipping a coin?

  1. 1/2

  2. 1/3

  3. 1/4

  4. 1/6
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 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

What are the properties of Brownian motion?

  1. It is a continuous-time process.

  2. It has independent increments.

  3. Its increments are normally distributed.

  4. All of the above
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Brownian motion is a continuous-time process, meaning that it can take on any value in a continuous interval. It has independent increments, meaning that the increments of the process are independent of each other. Its increments are normally distributed, meaning that the probability distribution of the increments is a normal distribution.

Multiple choice

What is a probability distribution?

  1. A function that describes the probability of a random variable taking on a particular value.

  2. A function that describes the probability of a random variable taking on a range of values.

  3. A function that describes the probability of a random variable taking on a set of values.

  4. A function that describes the probability of a random variable taking on a sequence of values.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A probability distribution is a function that describes the probability of a random variable taking on a particular value. Probability distributions are used in statistics, probability theory, and other applications.