Mathematics

Probability Distributions

488 Questions

Probability distributions describe the likelihood of different outcomes in a statistical experiment. Key topics include calculating confidence intervals, understanding Type II errors, and working with the standard normal distribution. These concepts are frequently tested in mathematics and statistics sections of various competitive exams.

Standard normal distributionType II error probabilityConfidence interval interpretationPoisson distributionProbability density function

Probability Distributions Questions

Multiple choice

What is the probability that a randomly selected person in India will travel by train?

  1. 0.1

  2. 0.2

  3. 0.3

  4. 0.4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the Indian Ministry of Railways, approximately 20% of all passenger trips in India are made by train.

Multiple choice

What is the probability that a randomly selected person in India will travel by air?

  1. 0.05

  2. 0.1

  3. 0.15

  4. 0.2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to the Directorate General of Civil Aviation, approximately 5% of all passenger trips in India are made by air.

Multiple choice

What is the probability that a randomly selected person in India will travel by car?

  1. 0.1

  2. 0.15

  3. 0.2

  4. 0.25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 20% of all passenger trips in India are made by car.

Multiple choice

What is the probability that a randomly selected person in India will travel by bicycle?

  1. 0.05

  2. 0.1

  3. 0.15

  4. 0.2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 10% of all passenger trips in India are made by bicycle.

Multiple choice

What is the probability that a randomly selected person in India will travel by foot?

  1. 0.1

  2. 0.15

  3. 0.2

  4. 0.25
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 25% of all passenger trips in India are made by foot.

Multiple choice

What is the probability that a randomly selected person in India will travel by more than one mode of transportation?

  1. 0.1

  2. 0.2

  3. 0.3

  4. 0.4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 20% of all passenger trips in India involve more than one mode of transportation.

Multiple choice

What is the probability that a randomly selected person in India will travel by a mode of transportation that is not listed in the options?

  1. 0.01

  2. 0.02

  3. 0.03

  4. 0.04
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

There are a number of modes of transportation that are not listed in the options, such as rickshaws, tongas, and bullock carts. According to the Indian Ministry of Road Transport and Highways, approximately 2% of all passenger trips in India are made by these modes of transportation.

Multiple choice

What is the probability that a randomly selected person in India will not travel at all?

  1. 0.1

  2. 0.2

  3. 0.3

  4. 0.4
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

According to the Indian Ministry of Road Transport and Highways, approximately 10% of all people in India do not travel at all.

Multiple choice

What is the probability that a randomly selected person in India will travel by a mode of transportation that is more efficient than a bus?

  1. 0.25

  2. 0.5

  3. 0.75

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

There are a number of modes of transportation that are more efficient than a bus, such as trains, airplanes, and cars. According to the Indian Ministry of Road Transport and Highways, approximately 50% of all passenger trips in India are made by these modes of transportation.

Multiple choice

What is the probability that a randomly selected person in India will travel by a mode of transportation that is less efficient than a bus?

  1. 0.25

  2. 0.5

  3. 0.75

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

There are a number of modes of transportation that are less efficient than a bus, such as bicycles, rickshaws, and tongas. According to the Indian Ministry of Road Transport and Highways, approximately 75% of all passenger trips in India are made by these modes of transportation.

Multiple choice

What is the probability that a randomly selected person in India will travel by a mode of transportation that is more expensive than a bus?

  1. 0.25

  2. 0.5

  3. 0.75

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

There are a number of modes of transportation that are more expensive than a bus, such as trains, airplanes, and cars. According to the Indian Ministry of Road Transport and Highways, approximately 50% of all passenger trips in India are made by these modes of transportation.

Multiple choice

What is the probability that a randomly selected person in India will travel by a mode of transportation that is less expensive than a bus?

  1. 0.25

  2. 0.5

  3. 0.75

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

There are a number of modes of transportation that are less expensive than a bus, such as bicycles, rickshaws, and tongas. According to the Indian Ministry of Road Transport and Highways, approximately 75% of all passenger trips in India are made by these modes of transportation.

Multiple choice

What is the use of partitions of sets in probability?

  1. To calculate the probability of an event.

  2. To calculate the expected value of a random variable.

  3. To calculate the variance of a random variable.

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

Partitions of sets are used in probability to calculate the probability of an event, the expected value of a random variable, and the variance of a random variable.

Multiple choice

What is the term for the probability of an event occurring given that another event has already occurred?

  1. Conditional Probability

  2. Joint Probability

  3. Marginal Probability

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

Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B).

Multiple choice

What is the term for the probability of two events occurring together?

  1. Conditional Probability

  2. Joint Probability

  3. Marginal Probability

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

Joint probability is the probability of two or more events occurring together. It is denoted as P(A and B).