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

In a binomial distribution with parameters 'n' and 'p', what is the probability of obtaining exactly '0' successes?

  1. (1-p)^n

  2. p^n

  3. n * p

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a binomial distribution with parameters 'n' and 'p', the probability of obtaining exactly '0' successes is given by (1-p)^n. This is because the probability of success is 'p' and the probability of failure is 1-p. To obtain exactly '0' successes, we need to have 'n' consecutive failures, which has a probability of (1-p)^n.

Multiple choice

What is the probability of obtaining at least one success in a sequence of 'n' independent Bernoulli trials with probability of success 'p'?

  1. 1 - (1-p)^n

  2. p^n

  3. n * p

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The probability of obtaining at least one success in a sequence of 'n' independent Bernoulli trials with probability of success 'p' is given by 1 - (1-p)^n. This is because the probability of obtaining exactly '0' successes is (1-p)^n, and the probability of obtaining at least one success is the complement of this, which is 1 - (1-p)^n.

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.

Multiple choice

What is the absorption probability of a state in a Markov Chain?

  1. The probability that a Markov Chain will eventually reach a state and never leave it.

  2. The probability that a Markov Chain will eventually leave a state and never return to it.

  3. The probability that a Markov Chain will reach a state and then leave it.

  4. The probability that a Markov Chain will leave a state and then return to it.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The absorption probability of a state in a Markov Chain is the probability that the chain will eventually reach that state and never leave it.

Multiple choice

What is the probability that a randomly selected person in India will travel by a mode of transportation that is more environmentally friendly 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 more environmentally friendly 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 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 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: head or tail. Since these outcomes are equally likely, the probability of getting a head is 1/2.

Multiple choice

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

  1. 0.5

  2. 0.25

  3. 0.75

  4. 0.1
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

For a fair coin, the probability of obtaining a head or a tail is equal, which is 0.5.

Multiple choice

What is a holed coin?

  1. When a coin has a hole in it

  2. When a coin is struck off-center

  3. When a coin is struck upside down

  4. When a coin is struck on the wrong coin
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Holed coins are coins that have a hole in them, either from being pierced or from being worn. Holed coins were often used as currency in the past, and they can be valuable to collectors today.

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 equally likely outcomes: heads or tails. Therefore, 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. 1/12

  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

Which mathematical field is closely associated with the study of randomness and probability in computer science?

  1. Algebra

  2. Analysis

  3. Probability theory

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

Probability theory, a branch of mathematics that deals with the study of randomness and probability, is extensively used in computer science for modeling and analyzing probabilistic algorithms, simulations, and random processes.