Using basic knowledge of probability, answer these questions about the chance of randomly answering them correctly.

**Average**, 10 Qns, Fi B, Dec 14 22

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These will be basic probability questions based on picking cards from a standard 52 card deck. Be careful, some questions involve conditional probability! Good luck! **Tough**, 10 Qns, rodney_indy,
Feb 28 17

What do you know about the science of statistics? A relatively easy quiz on basic concepts. **Tough**, 10 Qns, crisw,
Feb 02 23

This is a basic probability quiz. It involves coin flips, dice rolls, spinning spinners, and other things. Just remember, if you get stuck, make a logical guess! All answers will be expressed as common fractions. **Tough**, 10 Qns, xxharryxx,
Aug 03 22

A lot of people I know are a bit scared of statistics. But if you understand the basics, they can be very useful, and tell you lots of very interesting things about the world. Come on, have a play: you might be surprised how much you already know. **Average**, 10 Qns, timence,
Dec 24 13

All questions will deal with dice rolls. Be careful - some involve conditional probability! Good Luck! **Tough**, 10 Qns, rodney_indy,
Nov 06 21

A few questions to test your knowledge of mean, mode and median which are used frequently in statistics. Enjoy! **Average**, 10 Qns, Matthew_07,
Dec 02 10

This is a quiz on the language and basic results of probability that would be found in a course in finite mathematics. Good luck! **Tough**, 10 Qns, rodney_indy,
Sep 30 17

All of the questions in this quiz are questions on statistics and probability. **Average**, 10 Qns, AdamM7,
Feb 19 11

This quiz tests your knowledge on some basic probability theory concepts. Have fun and thanks for playing. **Tough**, 10 Qns, Matthew_07,
Jun 19 13

Quick Question

From Quiz "

Nothing is certain in this quiz. Test your calculation of probability. The questions are tricky, but can all be solved by logical thinking and a little bit of mathematics. E.g. a probability of 1/4 means one chance out of four, or 25%. **Tough**, 10 Qns, queenofsheba,
Apr 23 21

This quiz is on probabilities in popular games using dice including Craps, Yahtzee, Risk, and Monopoly. All of these games use standard six sided dice. Some of the answers may take a few minutes to calculate so I did not include a timed version. **Tough**, 10 Qns, andymuenz,
Jul 13 22

Ten probability questions based around FunTrivia. You might want a calculator handy for some questions and/or pen and paper ready for others. **Average**, 10 Qns, AdamM7,
Dec 28 21

Passing an Advanced Placement math test earns you college credit at most U.S. universities. How well would you do on a sample AP Statistics study guide test? Warning: statistics problems can be wordy! **Average**, 10 Qns, GBfan,
Dec 18 16

I will give a situation such as rolling dice or drawing cards, and ask the probability of a certain thing happening. **Difficult**, 10 Qns, iggy4,
Jan 20 16

I will explain a situation and ask the probability of a certain possibility occurring. **Very Difficult**, 10 Qns, iggy4,
Apr 26 22

In this quiz, I feature probability problems that I have related to real-life situations to make the questions applicable to daily life. Both finite and continuous distributions are reviewed. Some integration is needed for computing continuous examples. **Difficult**, 10 Qns, jrrymaury,
Dec 27 17

I say "Fun Trivia-Like" because of course only the folks at FunTrivia know the exact numbers involved. But if you have a little math savvy, you may enjoy this quiz on, well, quizzes.
**Tough**, 10 Qns, jbuck919,
Feb 08 17

The quiz is based on high school finite curriculum. For people who know finite math the quiz will be easy. **Tough**, 10 Qns, lanire,
Mar 18 19

Follow our friend Shelly through a pleasant, somewhat probable Sunday afternoon. No theoretical math knowledge is required for this quiz--logical guesses will suffice--though you're certainly likely to do better if you have some. Good luck! **Very Difficult**, 10 Qns, avrandldr,
Apr 12 10

Have you ever wondered how much you know about probability, the mathematical treatment of randomness of life? Take this quiz to find out! **Difficult**, 10 Qns, irving9918,
Dec 09 12

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?

Answer:

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.

2. In a ten question multiple choice (4 options) quiz on FunTrivia, you have a chance of roughly 0.0000954% to get all ten questions right guessing at random. How is this number calculated?

Answer:

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%

3. Craps is played with two dice. If you roll a 7 or an 11 on your first roll, you win. What are the chances that you win on your first roll?

Answer:

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.

4. One of the most common statistics worldwide is a periodic count of the population. What is this known as?

Answer:

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.

5. Combinatorics: Assume the balls are indistinguishable in all aspects except color. In an urn with 5 black balls and 3 white balls, how many ways can you pick 2 black balls and 1 white ball at once?

Answer:

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.

6. What is the probability of rolling 3 dice, and them all landing on a 6?

Answer:

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.

7. Suppose E and F are mutually exclusive events in a sample space S with probabilities .4 and .3 respectively. What is the probability of their union?

Answer:

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.

8. A card is selected at random from a standard 52 card deck. Assuming all cards are equally likely to be selected, what is the probability that a red king was selected?

Answer:

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.

9. Two six-sided dice are rolled. Find the probability the first die came up a 2 and the second die came up a 5.

Answer:

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.

10. There is a carnival game that requires you to roll two standard 6-sided dice. If the sum of the dice rolls is a prime number, then you win. What is the probability of winning?

Answer:

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.

11. What is the general formula for the factorial notation?

Answer:

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

12. Suppose E is an event in a sample space S with probability .3. What is the probability of the complement of E?

Answer:

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.

13. A card is selected at random from a standard 52 card deck. Assuming all cards are equally likely to be selected, what is the probability that a red card or a king was selected?

Answer:

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.

14. Two six-sided dice are rolled. Find the probability that one die came up a 2 and the other came up a 6.

Answer:

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

15. There is a standard 52-card deck. If you draw three cards randomly, without placing each back in the deck, what is the probability that all three cards are spades?

Answer:

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.

16. How can C(n,r) be represented in factorial form?

Answer:

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

17. When graphing a scatterplot of data points involving two variables, what do the letters LSRL stand for?

Answer:

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.

18. Lucky Ducky is a badge awarded to a random user who visits FunTrivia every day. If 100,000 players visit FunTrivia on one day, including myself, what is the chance that I will win the badge?

Answer:

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

19. House prices are followed closely by economists, who tend to favour a median (middle) measure rather than the mean (average). Why is that?

Answer:

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.

20. Suppose E and F are events in a sample space S. Suppose further that E has probability .2, F has probability .6, and the intersection of E and F has probability .1. What is the probability of the union of E and F?

Answer:

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.

21. A card is selected at random from a standard 52 card deck. Assuming all cards are equally likely to be selected, what is the probability that a red card was selected given that a king was selected?

Answer:

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.

22. Two six-sided dice are rolled. Find the probability that at least one die is a 3.

Answer:

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.

23. A box contains one of each of the bills: $1, $5, $10, $20, $50, and $100. If you randomly draw three bills, then what are the odds that the three bills add to $75?

Answer:

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.

24. What is the area under the curve of any probability distribution called?

Answer:

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."

25. How many different masses can be obtained using weights of mass 1kg, 2kg, 5kg, and 10kg?

Answer:

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.

26. While playing Yahtzee, what are the odds that, on your first throw for a turn, all five dice come up with the same number?

Answer:

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.

27. Statisticians can also look at possible future events to determine what changes are likely to a particular population. What are these predictions called?

Answer:

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.

28. Suppose E and F are independent events in a sample space S. Suppose further that E has probability .3 and F has probability .4. What is the probability of the intersection of E and F?

Answer:

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.

29. A card is selected at random from a standard 52 card deck. Assuming all cards are equally likely to be selected, what is the probability that a king was selected given that a red card was selected?

Answer:

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.

30. Two six-sided dice are rolled. Find the probability that the sum is 8.

Answer:

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.

This is category 7615

Last Updated Feb 25 2024 9:08 AM

Last Updated Feb 25 2024 9:08 AM

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