Statistics and Probability Trivia

1. The number of points scored in an NBA season for a team has the following statistics: Games played is 82, mean = 99.6, mode = 104, and median = 102. How would you describe a graph of this data?

From Quiz AP Statistics Study Guide

Answer: Skewed Left

If the mean equals the median, the graph would be a symmetrical distribution. But we know the mean follows the tail. In this scenario, the mean is lower than the median so this graph would be skewed left.

From Quiz Probability in FunTrivia

Answer: (1/4)^10

The chance of getting each question right is 1/4, or 0.25. You multiply these probabilities together to get the probability of getting all of them right: 1/4 * 1/4 * ... * 1/4 = (1/4)^10 = 1/1048576 = 0.000000954 = 0.0000954%

From Quiz Roll 'em Up

Answer: 2 in 9

Let's assume you have one red die and one blue die. Whatever number the red die shows, if the blue die lands on the opposite side, the two numbers will add up to 7. Thus there is a 1/6 chance of rolling a 7. In order to roll an 11, you need the red die to be either a 5 or a 6. There is a 1/3 chance of this. Once that happens, you have a 1/6 chance of the blue die being the other number that adds to 11. (The red die could be either a 5 or a 6 but the blue die can only be the one the red die is not.) 1/3 * 1/6 = 1/18. If we add the chances of a 7 (1/6) and an 11 (1/18) we get 3/18 + 1/18 = 4/18 or 2/9.

From Quiz Stat's Fantastic!

Answer: Census

Censuses have been carried out for thousands of years; one of the earliest recorded was the Census of Quirinius, taken during the the reign of Emperor Augustus in around 6 AD (and being linked to the Census that took Joseph and Mary to Bethlehem when Jesus was born). This Census was for gathering of taxes, but modern Censuses serve many more purposes, including helping decide where to locate essential services like public transport, schools and hospitals.

From Quiz Probability Theory

Answer: 30

There are (5 choose 2) = 5*4/2 = 10 ways to pick 2 black balls. There are 3 ways to pick 1 white ball. So there are a total of 10*3 = 30 ways to pick 2 black balls and 1 white ball.

From Quiz Simple Statistics

Answer: 1/216

Because there are 216 different combinations that 3 dice could land on, the probability is 1/216. There are 216 possible combinations because there are 6 combinations for 1 die ('die' is the singular name for 'dice') - 1 times 6, 36 combinations for 2 dice - 6 times 6, which means that the combinations for 3 dice are 6 times 6 times 6, or 6 cubed. 6 cubed is 216.

From Quiz Theoretical Basic Probability

Answer: 0.7

Mutually exclusive events are events whose intersection is the empty set. So the probability of their union is just the sum of their probabilities, which is .7.

From Quiz Pick A Card, Any Card!

Answer: 1/26

There are four kings in the deck - 2 are red and 2 are black. So the probability that a red king was selected is 2/52 = 1/26.

From Quiz Dice Probabilities

Answer: 1/36

There are 6 possibilities for the first die and 6 possibilities for the second die. Hence there are 6 * 6 = 36 possible dice rolls. There is only one of them: (2,5) which has 2 on the first die and 5 on the second die. Thus the probability is 1/36.

From Quiz Iggy's Probability Quiz

Answer: 5/12

There are 36 possible results from rolling two dice. The sum of the dice rolls will give you a number from 2 to 12. The prime numbers between them are 2, 3, 5, 7, and 11. The possible dice rolls to get those numbers are: 1-1, 1-2, 2-1, 1-4, 4-1, 2-3, 3-2, 1-6, 6-1, 2-5, 5-2, 4-3, 3-4, 6-5, and 5-6. Since there are 15 results that win the game, the odds of winning are 15/36, or 5/12.

From Quiz High School Finite Math

Answer: n*(n-1)*(n-2)*...*3*2*1

Factorial notation is generally represented by n! and involves consecutive numbers multiplied together in descending order until the number reaches one.

From Quiz Theoretical Basic Probability

Answer: 0.7

The probability of an event and its complement must sum to 1, since they are mutually exclusive and their union is the entire sample space S. So the probability of the complement of E is 1 - .3 = .7.

From Quiz Pick A Card, Any Card!

Answer: 7/13

Of the 52 cards in the deck, 26 are red, 4 are kings, and 2 are red kings. Hence the number of cards that are red or are a king are 26 + 4 - 2 = 28. We subtract 2 since the 2 red kings are being counted twice. So the probability that a red card or a king was selected is 28/52 = 7/13.

From Quiz Dice Probabilities

Answer: 1/18

This event consists of the outcomes (2,6), (6,2). Hence it has probability 2/36 = 1/18.

From Quiz Iggy's Probability Quiz

Answer: 11 out of 850

The probability of drawing one spade is 13/52 or 1/4. The odds of drawing another spade is 12/51. The odds of drawing a third spade is 11/50. If you multiply (1/4 * 12/51 * 11/50), you get 132/10200. This simplifies to 11/850.

From Quiz High School Finite Math

Answer: n! over (n-r)!r!

A combination is a choice of a number of elements from a given set without regard to order.

From Quiz AP Statistics Study Guide

Answer: least squares regression line

The least squares regression line helps identify if the data follows a linear pattern or not. From the LSRL we can compute the residual value using the formula: Residual = Observed value - Predicted LSRL value.

From Quiz Probability in FunTrivia

Answer: 0.00001

The chance of any particular player winning is 1/100,000. This is 0.00001 or 0.001%.

From Quiz Stat's Fantastic!

Answer: Very expensive houses bring the average up

The truth is that an average house price is not very meaningful because nowadays there are so many expensive houses dragging the number up. Medians are used in these sorts of 'skewed' data, because they offer a measure that tells you which number is in the middle of the distribution.

From Quiz Theoretical Basic Probability

Answer: 0.7

For any two sets, the probability of their union is just the sum of their probabilities, minus the probability of their intersection. This is called the principle of inclusion/exclusion. The reason you have to subtract the probability of the intersection is because the intersection of the two events is itself a subset of each event, so its probability gets counted twice. So the probability we're after is just .2 + .6 - .1 = .7.

From Quiz Pick A Card, Any Card!

Answer: 1/2

This is a conditional probability question. We are given that a king was selected. There are 4 kings in the deck. Of the 4 kings, 2 of them are red. So the probability that a red card was selected given that a king was selected is 2/4 = 1/2.

From Quiz Dice Probabilities

Answer: 11/36

The probability that the first die is 3 is 1/6, the probability that the second die is 3 is 1/6, and the probability that both dice are 3 is 1/36. By the principle of inclusion/exclusion, the probability that the first die or the second die is 3 is just 1/6 + 1/6 - 1/36 = 11/36. This probability is useful in backgammon - this is the probability of entering off the bar when there is only one open point in the opponent's table.

From Quiz Iggy's Probability Quiz

Answer: 1 in 20

You must draw $20, $5, and $50 since they are the only three bills that total $75. The odds of drawing one of the needed bills is 1/2. The odds of drawing another needed bill is 2/5. The odds of drawing the last needed bill is 1/4. When you multiply the three fractions, you get 2/40 or 1/20.

From Quiz The Mathematics of FunTrivia-Like Games

Answer: One square unit

The area under all probability distribution curves is considered to be one. Among other things, this facilitates calculating probability, which is always a number between zero and one. Lacking the means to draw the curve for you, I can only describe it as rising quickly to a maximum, then trailing off slowly with a long right "tail."

From Quiz High School Finite Math

Answer: 15

Number of possible weightings would be 2 to the power of 4 and then subtracted one because the case with no weightings taken is discounted.

From Quiz Roll 'em Up

Answer: 1 in 1296

There are two ways to look at this. One is to calculate the odds that each die is a 1. This is 1/6 * 1/6 * 1/6 * 1/6 * 1/6 = 1/7776. You can then see that the odds of any given number from 2-6 are the same. So the odds of them all being the same are 6/7776 or 1/1296. Alternatively, you could realize that it doesn't matter what number is on the first die, just that the other four have to match it and the odds for each of those is 1/6. So the odds of all four of the other dice matching the first are 1/6 * 1/6 * 1/6 * 1/6 = 1/1296.

From Quiz Stat's Fantastic!

Answer: Projections

According to the projections by "Internet World Stats" (based on various population Census counts), India will take over from China as the world's most populated country by 2050. It is estimated that India will have over 1.6 billion people by then, with China remaining relatively stable at 1.3 billion.

From Quiz Theoretical Basic Probability

Answer: 0.12

If E and F are independent events, the probability of their intersection is found by multiplying their respective probabilities. So the answer in this case is .3 * .4 = .12.

From Quiz Pick A Card, Any Card!

Answer: 1/13

This is a conditional probability question. We are given that a red card was selected. There are 26 red cards in the deck. Of the 26 red cards, 2 of them are kings. So the probability that a king was selected given that a red card was selected is 2/26 = 1/13.

From Quiz Dice Probabilities

Answer: 5/36

The outcomes in the event "the sum is 8" are: (2,6), (3,5), (4,4), (5,3), and (6,2). Since there are 5 ways the sum can be 8, the probability is 5/36.

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Last Updated Nov 16 2024 5:46 AM

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