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 general knowledge math & puzzles

A & B are two players. They select one number from 1 to 25. If both of them select the same number they will win. What is the probability of not winning in a single trial?

  1. 5/1

  2. 24/25

  3. 1/25

  4. 1/5
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The total number of possible outcomes when two people choose a number from 1 to 25 is 25 * 25 = 625. There are 25 outcomes where they choose the same number (1,1; 2,2; etc.). The probability of winning is 25/625 = 1/25. Therefore, the probability of not winning is 1 - 1/25 = 24/25.

Multiple choice general knowledge math & puzzles

The letters of the words AMERICAN PIES are placed in a bag. What is the probability that you will draw an E or an I if you chose one letter from the bag

  1. 1/4

  2. 1/3

  3. 1/8

  4. 5/12
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The phrase AMERICAN PIES has 12 total letters. Count the letters: A appears twice, E appears twice, and I appears twice. So there are 2 E's and 2 I's, giving 4 favorable outcomes out of 12 total letters. This simplifies to 1/3, which is the probability.

Multiple choice general knowledge

sachi and lachi are a married couple (dont ask me who he is and who she is)! They have two kids, one of them is a girl. Assume safely that the probability of each gender is 1/2. What is the probability that the other kid is also a girl?

  1. 1/3

  2. 2/3

  3. 1/2

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

This is a classic conditional probability puzzle. For a two-child family, the equally likely possibilities are: BB, BG, GB, GG (where B=boy, G=girl, and order matters). Given that at least one child is a girl, we eliminate BB, leaving three equally likely cases: BG, GB, GG. Only in GG are both children girls. Therefore, P(both girls | at least one girl) = 1/3. Option A is correct. The common mistake is thinking the answer is 1/2, which ignores that BG and GB are distinct cases.

Multiple choice general knowledge math & puzzles

4) The probabilities that a husband and wife will be alive 20 years from now are 0.8 and 0.9 respectively. Find the probability that in 20 years at least one will be alive.

  1. 0.26

  2. 0.76

  3. 0.86

  4. 0.36

  5. 0.98
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

The probability that at least one is alive is 1 minus the probability that both are dead. The probability the husband dies is 0.2 (1-0.8) and the wife dies is 0.1 (1-0.9). 1 - (0.2 * 0.1) = 1 - 0.02 = 0.98.

Multiple choice general knowledge math & puzzles

A group consists of equal number of men and women. Of them 10% of men and 45% of women are unemployed. If a person is randomly selected from the group. Find the probability for the selected person to be an employee?

  1. 29/40

  2. 26/40

  3. 25/40

  4. 23/40
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Assume 100 men and 100 women. Employed men = 90% of 100 = 90. Employed women = 55% of 100 = 55. Total employed = 145. Total people = 200. Probability = 145/200 = 29/40. Other fractions do not match this ratio.

Multiple choice general knowledge math & puzzles

Which of these numbers cannot be a probability?

  1. -0.00001

  2. 0.5

  3. 1.001

  4. 0

  5. 1
Reveal answer Fill a bubble to check yourself
A,C Correct answer
Explanation

Probabilities must be between 0 and 1 inclusive. Negative values (like -0.00001) and values greater than 1 (like 1.001) cannot represent probabilities because probability measures the likelihood of an event occurring on a scale from impossible (0) to certain (1).

Multiple choice general knowledge math & puzzles

The blood groups of 200 people is distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?

  1. 0.65

  2. 0.45

  3. 0.35

  4. 0.6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Probability is calculated as the number of favorable outcomes divided by the total number of outcomes. There are 70 people with type O blood out of a total of 200 people. $70 / 200 = 7 / 20 = 0.35$.

Multiple choice general knowledge

The probability that an electronic device produced by a company does not function properly is equal to 0.1. If 10 devices are bought, then the probability, to the nearest thousandth, that 7 devices function properly is

  1. 0.057

  2. 0.478

  3. 0.001

  4. 0
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is a binomial probability problem where success = device functions (p=0.9) and we want exactly 7 successes in 10 trials. Use the formula P(X=k) = C(n,k) * p^k * (1-p)^(n-k). C(10,7) = 120, so P = 120 * (0.9)^7 * (0.1)^3 ≈ 0.0574. The key is recognizing that 'functioning properly' probability is 0.9, not 0.1.

Multiple choice general knowledge science & technology

The rand( ) built-in library function?

  1. is a true random number generator.

  2. returns positive double values.

  3. is a pseudo-random number generator.

  4. returns a different sequence of values each time it is run.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

rand() is a pseudo-random number generator - it uses an algorithm to produce seemingly random numbers from a seed value. It produces the same sequence unless seeded with srand(). True randomness requires hardware entropy sources.

Multiple choice general knowledge science & technology

In the formula used for generating random numbers within a specific range (int number = a + rand( ) % n;), the n represents?

  1. the first value in the range of numbers.

  2. the last value in the range of numbers.

  3. the number of terms in the range of numbers.

  4. the number of guesses the user will be allowed.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

In the formula a + rand() % n, the modulo operation ensures the result ranges from 0 to n-1. So n represents the count of possible values. Adding a shifts the range to [a, a+n-1].