Mathematics

Probability Distributions

457 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 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 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).

Multiple choice

What is the term for the probability of an event occurring independently of any other event?

  1. Conditional Probability

  2. Joint Probability

  3. Marginal Probability

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

Independent probability is the probability of an event occurring independently of any other event. It is denoted as P(A) or P(B).

Multiple choice

What is the term for the probability of an event occurring?

  1. Conditional Probability

  2. Joint Probability

  3. Marginal Probability

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

Marginal probability is the probability of an event occurring. It is denoted as P(A) or P(B).

Multiple choice

What is the term for the probability of two events occurring independently of each other?

  1. Conditional Probability

  2. Joint Probability

  3. Marginal Probability

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

Independent probability is the probability of two events occurring independently of each other. It is denoted as P(A and B) = P(A) * P(B).

Multiple choice

What is the term for the probability of an event not occurring?

  1. Conditional Probability

  2. Joint Probability

  3. Marginal Probability

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

Marginal probability is the probability of an event occurring. It is denoted as P(A) or P(B). The probability of an event not occurring is 1 - P(A) or 1 - P(B).

Multiple choice

What is the probability of an event occurring?

  1. The ratio of favorable outcomes to possible outcomes

  2. The ratio of unfavorable outcomes to possible outcomes

  3. The ratio of favorable outcomes to unfavorable outcomes

  4. The ratio of possible outcomes to favorable outcomes
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Probability is a measure of the likelihood of an event occurring. It is calculated as the ratio of favorable outcomes to the total number of possible outcomes.

Multiple choice

What is the probability of an event not occurring?

  1. 1 - Probability of the event occurring

  2. Probability of the event occurring

  3. Probability of the event occurring + Probability of the event not occurring

  4. Probability of the event occurring - Probability of the event not occurring
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of an event not occurring is the complement of the probability of the event occurring. It is calculated as 1 minus the probability of the event occurring.

Multiple choice

What is the probability of two independent events occurring?

  1. Product of the probabilities of each event occurring

  2. Sum of the probabilities of each event occurring

  3. Difference of the probabilities of each event occurring

  4. Quotient of the probabilities of each event occurring
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of two independent events occurring is the product of the probabilities of each event occurring. This is because the occurrence of one event does not affect the probability of the other event occurring.

Multiple choice

What is the probability of two dependent events occurring?

  1. Product of the probabilities of each event occurring

  2. Sum of the probabilities of each event occurring

  3. Difference of the probabilities of each event occurring

  4. Quotient of the probabilities of each event occurring
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The probability of two dependent events occurring is the product of the probabilities of each event occurring, given the occurrence of the first event. This is because the occurrence of the first event affects the probability of the second event occurring.