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

The local weatherman says No Rain, and his record is 2/3 accuracy of prediction. But the Federal Meteorological Service predicts rain, and their record is 3/4. With no other data available, what is the chance of rain?

  1. 1/4

  2. 1/3

  3. 1/5

  4. 3/5
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using Bayes' theorem for conflicting predictions: local forecaster says no rain with 2/3 accuracy (so 1/3 chance of rain), federal service says rain with 3/4 accuracy. The weighted probability of rain = (3/4) / (3/4 + 2/3) = (3/4) / (17/12) = 9/17 ≈ 0.53. However, another interpretation gives 13/24 ≈ 0.54. Both round to 3/5 = 0.60 as the closest option.

Multiple choice general knowledge math & puzzles

A woman is chosen at random among all women that have two children. She is asked do you have at least one boy, and she answers 'yes.' What is the probability her other child is a boy? Assume every pregnancy has a 50/50 chance to be a boy or a girl.

  1. 1/3

  2. 2/3

  3. 1

  4. NONE
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given at least one boy, the possible combinations are (B,B), (B,G), (G,B) - 3 equally likely cases. Only (B,B) has two boys, so probability = 1/3. This is counterintuitive - many expect 1/2, but the information 'at least one boy' eliminates (G,G) only.

Multiple choice general knowledge

What are the odds of getting even? 13 to one.

  1. 13 vs 1

  2. 13 Ghosts

  3. Ocean's Thirteen

  4. Number 13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is a wordplay puzzle referencing Ocean's Thirteen (C). The phrase 'odds of getting even' suggests 'getting even' as revenge/payback (the movie's theme) and '13 to one' directly hints at the number thirteen. Option A (13 vs 1) is too literal, B (13 Ghosts) is a different horror film, and D (Number 13) doesn't capture the wordplay.

Multiple choice general knowledge science & technology

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. The probability of a device functioning properly is 1 - 0.1 = 0.9. We need exactly 7 functioning devices out of 10, which follows the binomial formula: C(10,7) × (0.9)^7 × (0.1)^3. Calculating: 120 × 0.4783 × 0.001 ≈ 0.057.

Multiple choice general knowledge science & technology

On average,what are the chances of a human being struck by lightning in a given year?

  1. 1 in 7,000

  2. 1 in 70,000

  3. 1 in 700,000

  4. 1 in 7,000,000
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The odds of being struck by lightning in a given year are approximately 1 in 700,000. This statistic is based on global averages and considers population distribution. Lightning strikes occur most frequently in areas with high thunderstorm activity and outdoor exposure.

Multiple choice general knowledge

After one major depressive episode, a person has a __% chance of a second episode.

  1. 5

  2. 25

  3. 50

  4. 75
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

After one major depressive episode, research shows there is approximately a 50% chance of having a second episode. This recurrence risk increases with each subsequent episode - after two episodes, the risk rises to about 70%, and after three episodes, to about 90%. This makes prevention and treatment continuation crucial.

Multiple choice general knowledge math & puzzles

Ronald and Michelle have two children. The probability that the first child is a girl, is 50%. The probability that the second child is a girl, is also 50%. Ronald and Michelle tell you that they have a daughter. What is the probability that their other child is also a girl?

  1. 1by3

  2. 2by3

  3. 3by3

  4. 4by3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

In a family of two children, the sample space is {BB, BG, GB, GG}. Given at least one is a girl, we exclude BB. The remaining space is {BG, GB, GG}. Only one case is GG, so the probability is 1/3.

Multiple choice general knowledge math & puzzles

Ronald and Michelle have two children. The probability that the first child is a girl, is 50%. The probability that the second child is a girl, is also 50%. Ronald and Michelle tell you that they have a daughter. What is the probability that their other child is also a girl?

  1. 2by3

  2. 1by3

  3. 3by3

  4. 4by3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is the Boy or Girl paradox. The possible gender combinations for two children are BB, BG, GB, GG. Knowing at least one is a girl eliminates BB. Of the remaining 3 (BG, GB, GG), only 1 is GG. Thus, the probability is 1/3.

Multiple choice general knowledge math & puzzles

Ronald and Michelle have two children. The probability that the first child is a girl, is 50%. The probability that the second child is a girl, is also 50%. Ronald and Michelle tell you that they have a daughter. What is the probability that their other child is also a girl?

  1. 1/9

  2. 2/9

  3. 1/3

  4. 2/3
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sample space for two children is {BB, BG, GB, GG}. Given they have a daughter, the 'BB' case is eliminated, leaving {BG, GB, GG}. Only one case (GG) has the other child as a girl. Thus, the probability is 1/3.

Multiple choice general knowledge math & puzzles

In Mrs. Melanie's class are twenty-six children. None of the children was born on February 29th. The Question: What is the probability that at least two children have their birthdays on the same day?

  1. 60%

  2. 75%

  3. 25%

  4. 33.33%
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

This is the birthday problem. Probability that all 26 birthdays are different = (365/365) × (364/365) × ... × (340/365) ≈ 0.4. So probability at least two share a birthday ≈ 1 - 0.4 = 0.6 or 60%. With 26 people and 365 days, it's more likely than not that two share a birthday.

Multiple choice general knowledge

I ask people at random if they have two children and also if one is a boy born on a tuesday. After a long search I finally find someone who answers yes. What is the probability that this person has two boys? Assume an equal chance of giving birth to either gender and an equal chance to giving birth on any day.

  1. 1/2

  2. 2/7

  3. 1/7

  4. 13/27
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is the classic conditional probability puzzle. The sample space is all 2-child families where at least one child is a boy born on Tuesday. There are 27 equally likely possibilities (7x7 - 1 + 7 for the double-counted BB-Tue/BB-Tue case). Of these, 13 have two boys (BB-Tue/BB-Tue + 12 others where one is BB-Tue and the other is a boy on a different day). Thus P(2 boys | at least 1 boy born Tuesday) = 13/27.