Ed answers probability and other math-related questions Strategy Page, math answers fast.#Math


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Number of times the coin was flipped 200 times: 5,000,000

Probability of a single event occurring: .5 (a fair coin)

Number of total times we will flip this coin: 200

Number of consecutive runs of heads we are looking for: 5

Number of times out of the total games played we saw our specified event occur: 4,829,647

The formula for the above is easy. For example, with three dice you do it this way: Multiply the chances of NOT

getting a one or a five (4/6) on the first die by the chances of NOT getting a one or a five on the second die (4/6) by the chances of NOT getting a one or a five on the third die, and the subtract the whole thing from 1.

1) The probability the number on the 5th die equals the number on the 7th die is 1/6 or 16.666% (The number on the 5th die has an equal chance of being 1 through 6. likewise with the 7th dice.)

2) There are 16 different “results,” all equally likely, after four coins are flipped:

2) Exactly four? 76,545 / 279,936 which reduces to 35/128 or 27.34375%.

I shouldn’t be doing your homework for you!

2-1, 2-2, 2-3, 2-4 , 2-5, 2-6, 2-7, 2-8, 2-9

3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 3-7, 3-8, 3-9

4-1, 4-2 , 4-3, 4-4, 4-5, 4-6, 4-7, 4-8, 4-9

2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7, 2-8, 2-9

3-1, 3-2 , 3-3, 3-4, 3-5, 3-6, 3-7, 3-8, 3-9

6 5 5 6 5 6 6 6 5 6 6 6

That’s the most incorrect statement I’ve read in this forum in awhile.

Team A loses 9 games out of 100 -$100 loss x 9 games = -$900

20/24 x 19/23 x 18/22 x 17/21 = .45595. about 45.59%.

What is the probability that none of them are yellow?

– Jake always has to use the bathroom so he must sit on one of the ends.

– Justin Jane don’t get along and need to have at least two seats between them.

– Jane Julie are best friends and insist on sitting next to each other.

– Jesse has a crush on Jessica and wants to sit next to her, but he can’t sit next to Jordan (after all, Jordan Jessica did just break up.)

– Joey needs to sit in one of the two middle seats.

1 5 6 8 2 7 4 3 1 5 6 8 4 2 7 3 1 5 6 8 4 7 2 3 1 5 6 8 7 2 4 3

1 6 5 8 2 7 4 3 1 6 5 8 7 2 4 3 2 7 4 1 8 5 6 3 2 7 4 1 8 6 5 3

2 7 4 8 1 5 6 3 2 7 4 8 1 6 5 3 2 7 4 8 6 5 1 3 2 7 5 6 8 1 4 3

2 7 5 6 8 4 1 3 2 7 6 5 8 1 4 3 3 1 4 8 2 7 5 6 3 1 4 8 2 7 6 5

3 1 4 8 6 5 2 7 3 1 4 8 6 5 7 2 3 1 4 8 7 2 5 6 3 1 4 8 7 2 6 5

3 1 5 6 8 2 7 4 3 1 5 6 8 4 2 7 3 1 5 6 8 4 7 2 3 1 5 6 8 7 2 4

3 1 6 5 8 2 7 4 3 1 6 5 8 7 2 4 3 2 7 4 8 1 5 6 3 2 7 4 8 1 6 5

3 2 7 4 8 6 5 1 3 2 7 8 4 1 6 5 3 2 7 8 5 6 1 4 3 4 1 8 2 7 5 6

3 4 1 8 2 7 6 5 3 4 1 8 5 6 2 7 3 4 1 8 5 6 7 2 3 4 1 8 6 5 2 7

3 4 1 8 6 5 7 2 3 4 1 8 7 2 5 6 3 4 1 8 7 2 6 5 3 4 2 7 8 1 5 6

3 4 2 7 8 1 6 5 3 4 2 7 8 5 6 1 3 4 2 7 8 6 5 1 3 4 7 2 8 1 5 6

3 4 7 2 8 1 6 5 3 4 7 2 8 5 6 1 3 4 7 2 8 6 5 1 3 5 6 1 8 2 7 4

3 5 6 1 8 4 2 7 3 5 6 1 8 4 7 2 3 5 6 1 8 7 2 4 3 5 6 8 1 4 2 7

3 5 6 8 1 4 7 2 3 5 6 8 2 7 4 1 3 5 6 8 7 2 4 1 3 6 5 1 8 2 7 4

3 6 5 1 8 4 2 7 3 6 5 1 8 4 7 2 3 6 5 1 8 7 2 4 3 6 5 8 1 4 2 7

3 6 5 8 1 4 7 2 3 6 5 8 2 7 4 1 3 6 5 8 7 2 4 1 3 7 2 4 8 1 5 6

3 7 2 4 8 1 6 5 3 7 2 4 8 6 5 1 3 7 2 8 4 1 6 5 3 7 2 8 5 6 1 4

4 1 6 5 8 2 7 3 4 1 6 5 8 7 2 3 4 2 7 8 1 5 6 3 4 2 7 8 1 6 5 3

4 2 7 8 5 6 1 3 4 2 7 8 6 5 1 3 4 7 2 8 1 5 6 3 4 7 2 8 1 6 5 3

4 7 2 8 5 6 1 3 4 7 2 8 6 5 1 3 5 6 1 4 8 2 7 3 5 6 1 4 8 7 2 3

5 6 1 8 2 7 4 3 5 6 1 8 4 2 7 3 5 6 1 8 4 7 2 3 5 6 1 8 7 2 4 3

5 6 2 7 8 1 4 3 5 6 2 7 8 4 1 3 5 6 7 2 8 1 4 3 5 6 7 2 8 4 1 3

6 5 1 8 2 7 4 3 6 5 1 8 4 2 7 3 6 5 1 8 4 7 2 3 6 5 1 8 7 2 4 3

6 5 2 7 8 1 4 3 6 5 2 7 8 4 1 3 6 5 7 2 8 1 4 3 6 5 7 2 8 4 1 3

7 2 4 1 8 5 6 3 7 2 4 1 8 6 5 3 7 2 4 8 1 5 6 3 7 2 4 8 1 6 5 3

7 2 4 8 6 5 1 3 7 2 5 6 8 1 4 3 7 2 5 6 8 4 1 3 7 2 6 5 8 1 4 3

2 1 5 2 5 1 3 1 4 3 4 1

4 1 3 4 3 1 5 1 2 5 2 1

1 – .2953782 = .7046218.

34.15% of the time you will lose $2,000

Sorry for not getting back to you earlier. I’ve been busy in a chess tournament all weekend, out of town. I just got home.

EVERYONE, at one time or another comes up with this idea / system, yours truly included. Often it’s for Roulette, or Blackjack, but it can be used for any game, including Craps.

Losing rolls: 1-3, 3-1, 2-2

As far as systems go, it’s no better or no worse than any other type of system. But there is no way to bet, or manner of betting that will put the odds in your favor. In your case, you will break even in the long run. again, because there is no house edge, when laying 2 to 1 on a true 2 to 1 proposition.

The one problem with the above, and correct me if I’m wrong, is that these bets are made AFTER a point is established. But you’re not allowed to just walk up to a table and wait for a point to be established and do this. You have to first bet on the pass or don’t pass bet. Only then can you bet on the 4 point making it or not, and taking the odds. (True odds, in this case.) And that amount that you can bet on these rolls after a point is established is limited to that particular casino. (That’s the triple odds and quadruple odds and ten times odds and stuff I can recall seeing on marquees.)

Hope this helps. at least a little bit. Good luck in your Crap playing. May the dice be with you. 🙂

Assume the following:

A total of ten, twelve-sided dice are rolled. seven attacking dice and three defending dice.

In order for a kill to occur, three (or more) 12s must be rolled from the seven attacking dice. However, for every 1 that is rolled on the attacking dice, this cancels out a 12.

For every 12 that is rolled on the defending dice, this also cancels out a 12 on the attacking dice.

To clarify, there must be at least three 12s remaining on the seven attacking dice, after subtracting one 12 for every 1 that is rolled on the seven attacking dice, and for every 12 that is rolled on the three defending dice.

The probability is exactly 0.00877970848425242. This is verified by first a computer simulation, over 1 billion trials, and then simply by examining all possible ways to roll ten, 12-sided dice.

There are exactly 61,917,364,224 ways to roll ten 12-sided dice. (12^10) According to a program I wrote that examines each roll and determines if a kill occurred, (that takes several minutes to run), exactly 543,616,408 of these rolls have three or more 12s remaining. 543,616,408 divided by 61,917,364,224 is exactly .00877970848425242, which verifies the simulation.

What is the probability of the sum of a pair of six-sided dice equaling either 2, 3, 4, 9, 10, 11, or 12 at least once in ten rolls?

There are 36 different ways two, 6-sided dice can be rolled. There a total of 16 suitable outcomes and 20 non-suitable outcomes.

The only way I know of to solve this problem is to write a program to loop through all possible two and three digit numbers, multiplying them together, looking for the given criteria. I did so and the program returns the following:

27 x 594 = 16,038

36 x 495 = 17,820

39 x 402 = 15,678

45 x 396 = 17,820

46 x 715 = 32,890

52 x 367 = 19,084

54 x 297 = 16,038

63 x 927 = 58,401

78 x 345 = 26,910

Notice only one of the products is odd. That might make for a good math puzzle.

I came across your site while looking for some help to a statistics assignment that has me all stressed out. It is not all that difficult but I am having a hard time. I am taking virtual classes for college, this is my last semester to graduate, but my first doing online classes, since I just moved and I needed the flexibility. I miss having a teacher to ask questions to. The system here is pretty weird – they just don’t seem to care and when you have doubts it is kind of your own problem. So here I am, reaching to you to see if maybe you can help.

This is the assignment:

Imagine yourself at a fair playing one of the midway games. Pick a game and calculate the expected value and post your results along with how you calculated them. For example, you may decide to throw a basketball to try to win a $10 bear. You paid $2.00 for three shots. What is the expected value? (Please do not use this example in your answer)

And so I came up with this example (which if you honestly think it sucks, if you can help me change it, if needed, it would be great).

I would like to thank you in advance.

I hope to hear from you soon!

Expected Value = (Cost to play the game x the chance of losing) + (the gain if you win x the chance of winning)

Here’s further proof the formula works. Maybe you’re familiar with the casino game of roulette. A quick Google search will tell you the house percentage for roulette is .0526. That’s the house edge, so expressed differently, the percentage against the player is – .0526.

I said earlier I would explain more about why I didn’t like the two games in your e-mail. (The game you proposed and the game in the assignment example. There is no way to determine the Expected Value. There is no way to determine the exact odds of winning.


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  • Math Word Problems with Answers – Grade 8, math answers fast.#Math #answers


    Free Mathematics Tutorials

    Grade 8 math word problems with answers are presented. Also solutions and explanations are included.

  • A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?

  • In a group of 120 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person’s age is less than 20?

  • A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?

  • Point A has the coordinates (2,2). What are the coordinates of its image point if it is translated 2 units up and 5 units to the left, and reflected in the x axis?

  • The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?

  • Each dimension of a cube has been increased to twice its original size. If the new cube has a volume of 64,000 cubic centimeters, what is the area of one face of the original cube?

  • Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).

  • A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.

  • Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?

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  • Water is being pumped, at a constant rate, into an underground storage tank that has the shape of a rectangular prism. Which of the graphs below best represent the changes in the height of water in the tank as a function of the time?

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  • Initially the rectangular prism on the left was full of water. Then water was poured in the right cylindrical container so that the heights of water in both containers are equal. Find the height h of water in both containers.(round your answer to the nearest tenth of a cm).

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  • Peter drove at a constant speed for 2 hours. He then stopped for an hour to do some shopping and have a rest and then drove back home driving at a constant speed. Which graph best represents the changes in the distance from home as Peter was driving?

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  • Two balls A and B rotate along a circular track. Ball A makes 2 full rotations in 26 minutes. Ball B makes 5 full rotation in 35 minutes. If they start rotating now from the same point, when will they be at the same starting point again?

  • In a certain college, 40% of the senior class students is taking Physics, 30% is taking calculus and 10% is taking both. If 40 students are enrolled in the senior class, how many students are taking neither Physics nor calculus?

  • Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same distance. What is the average speed for the whole trip?

  • If the radius of a cylindrical container is doubled, how do you change the height of the container so that the volume will stay the same?

  • One leg of a right triangle is 18 cm and its area is 108 square cm. Find its primeter.

  • What is the sum of the sizes of the interior angles of a polygon with 53 sides?

  • Jack is taller than Sarah but shorter than both Malika and Tania. Malika is shorter than tania. Natasha is shorter than Sarah. Who is the shortest?

  • What is the height (one of the legs) and the hypotenuse of an isosceles right triangle that has an area of 800 square feet?

  • Find the circumference of a circle inscribed inside a square with a side of 20 meters.

  • Two different schools (A and B) have the same number of pupils. The ratio of the boys in school A and the boys in school B is 2:1 and the ratio of the girls in school A and the girls in school B is 4:5. Find the ratio of the boys in school A to the girls in school A.

  • A water tank has the shape of a rectangular prism of base 50 cm 2 . This tank is being filled at the rate of 12 liters per minutes. Find the rate at which the height of the water in the water tank increases; express your answer in millimeters per second.

  • One pump fills a tank two times as fast as another pump. If the pumps work together they fill the tank in 18 minutes. How long does it take each pump working alone to fill the tank?

    Answers to the Above Questions

    1. 60 miles per hour
    2. 0.25
    3. 20 meters
    4. 1/3
    5. (-3,-4)
    6. 300 square meters
    7. 400 square cm
    8. 3 hours and 5 minutes
    9. 10 cm per minute
    10. 12 cards at $0.25 and 8 cards at $0.15
    11. 618.75 square cm
    12. graph at the bottom left
    13. 7.2 cm
    14. graph at the bottom left
    15. After 1 hour and 31 minutes
    16. 16 students
    17. 49.5 miles per hour
    18. 1/4 of the original height
    19. 51.6 cm
    20. 9180 degrees
    21. Natasha
    22. height (leg) = 40 feet , hypotenuse = 40 sqrt(2) feet
    23. 20pi meters
    24. ratio of the boys in school A to the girls in school A is 1:2
    25. 40 mm/second
    26. faster pump: 27 minutes, slower pump: 54 minutes

  • Math Word Problems with Answers – Grade 8, math answers fast.#Math #answers


    Free Mathematics Tutorials

    Grade 8 math word problems with answers are presented. Also solutions and explanations are included.

  • A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour?

  • In a group of 120 people, 90 have an age of more 30 years, and the others have an age of less than 20 years. If a person is selected at random from this group, what is the probability the person’s age is less than 20?

  • A six-sided die is rolled once. What is the probability that the number rolled is an even number greater than 2?

  • Point A has the coordinates (2,2). What are the coordinates of its image point if it is translated 2 units up and 5 units to the left, and reflected in the x axis?

  • The length of a rectangle is increased to 2 times its original size and its width is increased to 3 times its original size. If the area of the new rectangle is equal to 1800 square meters, what is the area of the original rectangle?

  • Each dimension of a cube has been increased to twice its original size. If the new cube has a volume of 64,000 cubic centimeters, what is the area of one face of the original cube?

  • Pump A can fill a tank of water in 5 hours. Pump B can fill the same tank in 8 hours. How long does it take the two pumps working together to fill the tank?(round your answer to the nearest minute).

  • A water tank, having the shape of a rectangular prism of base 100 square centimeters, is being filled at the rate of 1 liter per minute. Find the rate at which the height of the water in the water tank increases. Express your answer in centimeters per minute.

  • Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?

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  • Water is being pumped, at a constant rate, into an underground storage tank that has the shape of a rectangular prism. Which of the graphs below best represent the changes in the height of water in the tank as a function of the time?

    Math answers fast Math answers fast Math answers fast .

  • Initially the rectangular prism on the left was full of water. Then water was poured in the right cylindrical container so that the heights of water in both containers are equal. Find the height h of water in both containers.(round your answer to the nearest tenth of a cm).

    Math answers fast Math answers fast Math answers fast .

  • Peter drove at a constant speed for 2 hours. He then stopped for an hour to do some shopping and have a rest and then drove back home driving at a constant speed. Which graph best represents the changes in the distance from home as Peter was driving?

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  • Two balls A and B rotate along a circular track. Ball A makes 2 full rotations in 26 minutes. Ball B makes 5 full rotation in 35 minutes. If they start rotating now from the same point, when will they be at the same starting point again?

  • In a certain college, 40% of the senior class students is taking Physics, 30% is taking calculus and 10% is taking both. If 40 students are enrolled in the senior class, how many students are taking neither Physics nor calculus?

  • Joe drove at the speed of 45 miles per hour for a certain distance. He then drove at the speed of 55 miles per hour for the same distance. What is the average speed for the whole trip?

  • If the radius of a cylindrical container is doubled, how do you change the height of the container so that the volume will stay the same?

  • One leg of a right triangle is 18 cm and its area is 108 square cm. Find its primeter.

  • What is the sum of the sizes of the interior angles of a polygon with 53 sides?

  • Jack is taller than Sarah but shorter than both Malika and Tania. Malika is shorter than tania. Natasha is shorter than Sarah. Who is the shortest?

  • What is the height (one of the legs) and the hypotenuse of an isosceles right triangle that has an area of 800 square feet?

  • Find the circumference of a circle inscribed inside a square with a side of 20 meters.

  • Two different schools (A and B) have the same number of pupils. The ratio of the boys in school A and the boys in school B is 2:1 and the ratio of the girls in school A and the girls in school B is 4:5. Find the ratio of the boys in school A to the girls in school A.

  • A water tank has the shape of a rectangular prism of base 50 cm 2 . This tank is being filled at the rate of 12 liters per minutes. Find the rate at which the height of the water in the water tank increases; express your answer in millimeters per second.

  • One pump fills a tank two times as fast as another pump. If the pumps work together they fill the tank in 18 minutes. How long does it take each pump working alone to fill the tank?

    Answers to the Above Questions

    1. 60 miles per hour
    2. 0.25
    3. 20 meters
    4. 1/3
    5. (-3,-4)
    6. 300 square meters
    7. 400 square cm
    8. 3 hours and 5 minutes
    9. 10 cm per minute
    10. 12 cards at $0.25 and 8 cards at $0.15
    11. 618.75 square cm
    12. graph at the bottom left
    13. 7.2 cm
    14. graph at the bottom left
    15. After 1 hour and 31 minutes
    16. 16 students
    17. 49.5 miles per hour
    18. 1/4 of the original height
    19. 51.6 cm
    20. 9180 degrees
    21. Natasha
    22. height (leg) = 40 feet , hypotenuse = 40 sqrt(2) feet
    23. 20pi meters
    24. ratio of the boys in school A to the girls in school A is 1:2
    25. 40 mm/second
    26. faster pump: 27 minutes, slower pump: 54 minutes

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    1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

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    2. A sports field is 300 feet long. Write a formula that gives the length of x sports fields in feet. Then use this formula to determine the number of sports fields in 720 feet.

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    4. Mario answered 30% of the questions correctly. The test contained a total of 80 questions. How many questions did Mario answer correctly?


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