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Grade 7 POTW: Since each dice has 6 sides, I can use 6x6 to get 36, and that is the total amount of different possibilities. This is much easier than counting each different solution. The maximum sum that can be rolled is 18, so the squares and prime numbers have to be smaller or equal to 18. The squares that are smaller than 18 are 1, 4, 9, and 16. The prime numbers that are smaller than 18 are 2, 3, 5, 7, 11, 13, and 17. Now, I find different values that add up to these numbers. But, before I start, I also have to eliminate impossible sums. It is impossible to do 1, because the smallest sum is 2. It is also impossible to do 13 or 17 because there are no two numbers on the dice that can add up to them. So, I am left with 2, 3, 4, 5, 7, 9, 11, and 16. There are no overlap of numbers so whatever values I figure out I add together and create a fraction with.
For 2, there is only one possible value: 1+1. For 3, there are two possible values: 1+2 and 2+1(Works because dice one can be 1, dice 2 can be two, and vice versa. Two different solutions) For 4, there are 3 different solutions: 1+3, 2+2, 3+1. For 5, there are two different solutions: 3+2 and 2+3. For 7, there are 2 different solutions: 2+5 and 5+2. For 9, there are 2 different solutions: 2+7 and 7+2. For 11, there are two different solutions: 2+9 and 9+2. For 16, there are two different solutions: 9+7 and 7+9. I add all of the different solutions up to get a total sum of 16, since 1+2+3+2+2+2+2+2 = 16. The fraction would be 16/32, which in simplest terms would be 1/2. The chance of winning is 1/2. Alan
The answer to Gr.7 potw is that it's a 4 out of 9 chance you win. So what you do is create a chart of all possible rolls that can come out (1: 2, 3, 4, 6, 8, 10 2: 3, 4, 5, 7, 9, 11 3: 4, 5, 6, 8, 10, 12 5: 6, 7, 8, 10, 12, 14 7: 8, 9, 10, 12, 14, 16 9: 10, 11, 12, 14, 16, 18) And out of all of those 16 of them are squares out of all 36 options and it's simplified to 4 out of 9.
To find the answer, you have list all of the possible outcomes, and if the winning combinations are squares, then 16 of 36 are correct, which if reduced, is 4 of 9
GRADE 7: I concluded by finding all possible combinations that the are 7 perfect squares and 9 prime numbers therefore, the totals are: 16 out of 36, 8 out of 18 or, 4 out of 9. GRADE 8: The answer is 3 out of 36 or 1 out of 12. I looked at both possibilities and combined them. From: Luke
By doing a chart, you could find all the possibilities, which is 36 1: 1,2,3,5,7,9 2: 1,2,3,5,7,9 3: 1,2,3,5,7,9 etc. After, I had to find all the sums of each number and see what they add all up to, and then decide on which sums are prime or perfect squares. This includes: 1: 2,3,4,6,8,10 2: 3,4,5,7,9,11 3: 4,5,6,8,10,12 5: 6,7,8,10,12,14 7: 8,9,10,12,14,16 9: 10,11,12,14,16,18 Next, we have to find all the different perfect squares and prime numbers: Prime numbers: 2,3,5,7,9,11,13,17,19 Perfect Squares: 4,9,16, 25 Numbers that are prime or perfect squares: 2,3,3,4,4,4,5,5,7,7,9,9,11,11,16,16 The fraction for this question would be 16/36 or 4/9
Here is how I went about solving the Grade 7 POTW: If we make a chart of some sort, we can tell that there are 36 possible outcomes. How I came up with this number is by simply doing 6 multiplied by 6 and that creates a product of 36. We can only use numbers up to 18 because that is the maximum sum that you can get from rolling both dice. But if we dig deeper into this, we find that the numbers 4, 9 and 16 appear a total of 7 times (the perfect squares). Then we also see the prime numbers are 2, 3, 5, 7, and 11. These numbers appear a total of 9 times. Then I realized that it is not possible for the sum of the digits on the two dice to be both a prime number and a perfect square. So by knowing this we can make sure that the sum has not been repeated. So we take the total amount of prime numbers (7), and the total amount of perfect squares (9), and we add them. That gives us a total of 16. Finally, to find the probability of winning we would divide 16 by 36 (the amount of possible outcomes) and we get a fraction of 4/9. When this is converted into a percentage, it is 44%. Therefore, the probability of winning on any particular roll, is 44%.
Grade 8 POTW: I'm not actually very sure about this answer. I think that the answer is 1/9. I think this way because there is a 2/6 or 1/3 of rolling an odd number on the first roll, and a 4/6 or 2/3 chance of an even number. If the number was even on the first roll, there would be a 1/6 chance of getting a 2. I multiply it and get 1/9. If the number was odd on the first roll, there would be a 1/3 chance of getting a 2. I multiply this and get 1/9. So, the chance should be 1/9. Alan
Grade 7 POTW: I know that there are 36 possible outcomes because there are 6 numbers on each die and 6x6=36. I made a chart to see all the possible outcomes:
Out of these 36 outcomes, 16 are perfect squares or prime numbers. Therefore, you would have a 16/36 or 4/9 chance of winning on any particular roll.
To find the percent of winning, you would need to divide 16 by 36 or 4 by 9 and you would get 0.4444 and so on which would round 44.5%. The percent of winning on any particular roll is 44.5%.
Grade 7 POTW: So first we know that there are 36 outcomes from rolling. Within these outcomes only 16 are either perfect squares or prime numbers. That means that you have a 16/36 chance or winning. Simplified to 4/9 chances of winning the game. The percentage would be 44%. ~Michelle
Grade 7 POTW #3: First, we need to figure out how many possibilities there are. There are 6 numbers on each die so 6 x 6 = 36. That means there 36 possible outcomes. Now, we make a chart so we can figure out which are perfect squares or prime numbers. 1: 2, 3, 4, 6, 8, 10 2: 3, 4, 5, 7, 9, 11 3: 4, 5, 6, 8, 10, 12 5: 6, 7, 8, 10, 12, 14 7: 8, 9, 10, 12, 14, 16 9: 10, 11, 12, 14, 16, 18
There are 4 perfect squares, which are 4, 9, 16 and 25. There are 9 prime numbers, which are 2, 3, 5, 7, 9, 11, 13, 17, 19. There are 16 prime numbers and perfect squares in total. 16 out of 36. Or 4 out of 9. Therefore, the probability is 4/9.
Grade 7 POTW First, we must find all possible outcomes, and because there is 6 numbers on each die, and there are 2 dies, 6x6=36. To find all the prime and square numbers, I created a chart. 1:2,3,4,6,8,10 2:3,4,5,7,9,11 3:4,5,6,8,10,12 5:6,7,8,10,12,14 7:8,9,10,12,14,16 9:10,11,12,14,16,18
As you can see, there are 4 perfect squares (4,9,16,25) and 9 prime number (2,3,5,7,9,11,13,17,19). In total, there are 16 prime and square numbers. This means that you have a 16/36 chance of winning, which is simplified to 4/9. Therefore, the chance or probability is 4/9.
Unfortunately, my work was randomly deleted by blogger once, and then i redid it but it was deleted once again, so I did not want to redo the work again. My method of solving this problem was to create a chart of all the possibilities, and then find the prime numbers/perfect squares in this chart.
First we need to find all of the possible outcomes and then single out the answers which fit into the criteria. since there are six sides with number and 2 die, there are 36 possible outcomes (6x6=36 1: 2,3,4,6,8,10 2: 3,4,5,7,9,11 3: 4,5,6,8,10,12 5: 6,7,8,10,12,14 7: 8,9,10,12,14,16 9: 10,11,12,14,16,18
IF you count there would be a total of 36 different outcomes. Now we just have to take out the prime and perfect square. There are 4 perfect squares (4,9,16 and 25) and 9 prime numbers (2,3,5,7,9,11,13,17,19). When we add those two numbers we would get 16. That means the fraction would be 16/36. This can also be changed to 4/9.
First we need to find all of the possible outcomes and then single out the answers which fit into the criteria. since there are six sides with number and 2 die, there are 36 possible outcomes (6x6=36 1: 2,3,4,6,8,10 2: 3,4,5,7,9,11 3: 4,5,6,8,10,12 5: 6,7,8,10,12,14 7: 8,9,10,12,14,16 9: 10,11,12,14,16,18
IF you count there would be a total of 36 different outcomes. Now we just have to take out the prime and perfect square. There are 4 perfect squares (4,9,16 and 25) and 9 prime numbers (2,3,5,7,9,11,13,17,19). When we add those two numbers we would get 16. That means the fraction would be 16/36. This can also be changed to 4/9.
Grade 7 POTW (I was confused by perfect squares, so I just used a chart I found from the internet to help me) I first listed out all of the possibilities! I would do a tree diagram but I have no way to show it on technology.
Now we have 36 outcomes now we have to find the perfect squares and prime numbers, after using the chart to help me I figured: 4,9,16,25 are perfect squares 2,3,5,7,9,11 are the prime numbers
The answer that I got for the magic cube was 2/9. I got this by first listing the total combinations and outcomes. Basically with two different conditions there were two possible chances of cubes. 1,1,3,2,3,4 if landed on even and 2,2,6,4,6,8 if landed on odd.Also i put in the fact it is a 2/6 chance to get an odd number compared to a 4/6 chance to get an even number. With that information I was able to come up with the total combinations of rolls. 12 possible combinations were possible with odd numbers and 24 possible combinations were possible with even numbers. Thus giving me the total of 36 possibilities. With that I counted how many combinations have 2 at the end which is 8 thus giving me 8/36 which reduced is 2/9.
To solve this potw I fist looked at the rules, if you roll an even all even numbers are halved and if you role an odd, they are all doubled, so I wrote out all of the possibility's for the first role; 1: 2 6 2 4 6 8 2: 1 2 3 4 1 3 3: 2 6 2 4 6 8 4: 1 2 3 4 1 3 6: 1 2 3 4 1 3 8: 1 2 3 4 1 3 There where 36 possibility's for the first role and since the second does not count we can ignore it, out of those roles there are 8 twos so it is 8/36, but this can be made into 2/9 at the smallest, so the chance of rolling a 2 on the second roll is 2/9
How many students obtained the correct answer for the POTW #2 Grade 8 question?
ReplyDeleteI got both questions right... YAY! :)
DeleteI got both correct! My life is complete! O.o
DeleteI did!! I think...
DeleteGrade 7 POTW:
ReplyDeleteSince each dice has 6 sides, I can use 6x6 to get 36, and that is the total amount of different possibilities. This is much easier than counting each different solution.
The maximum sum that can be rolled is 18, so the squares and prime numbers have to be smaller or equal to 18.
The squares that are smaller than 18 are 1, 4, 9, and 16.
The prime numbers that are smaller than 18 are 2, 3, 5, 7, 11, 13, and 17.
Now, I find different values that add up to these numbers.
But, before I start, I also have to eliminate impossible sums. It is impossible to do 1, because the smallest sum is 2. It is also impossible to do 13 or 17 because there are no two numbers on the dice that can add up to them. So, I am left with 2, 3, 4, 5, 7, 9, 11, and 16. There are no overlap of numbers so whatever values I figure out I add together and create a fraction with.
For 2, there is only one possible value: 1+1.
For 3, there are two possible values: 1+2 and 2+1(Works because dice one can be 1, dice 2 can be two, and vice versa. Two different solutions)
For 4, there are 3 different solutions: 1+3, 2+2, 3+1.
For 5, there are two different solutions: 3+2 and 2+3.
For 7, there are 2 different solutions: 2+5 and 5+2.
For 9, there are 2 different solutions: 2+7 and 7+2.
For 11, there are two different solutions: 2+9 and 9+2.
For 16, there are two different solutions: 9+7 and 7+9.
I add all of the different solutions up to get a total sum of 16, since 1+2+3+2+2+2+2+2 = 16. The fraction would be 16/32, which in simplest terms would be 1/2.
The chance of winning is 1/2.
Alan
Correction to my last post:
ReplyDeleteI accidently put down 16/32 when it should have been 16/36.
So, in simplest forms, the answer is actually 4/9.
Alan
The answer to Gr.7 potw is that it's a 4 out of 9 chance you win. So what you do is create a chart of all possible rolls that can come out
ReplyDelete(1: 2, 3, 4, 6, 8, 10
2: 3, 4, 5, 7, 9, 11
3: 4, 5, 6, 8, 10, 12
5: 6, 7, 8, 10, 12, 14
7: 8, 9, 10, 12, 14, 16
9: 10, 11, 12, 14, 16, 18)
And out of all of those 16 of them are squares out of all 36 options and it's simplified to 4 out of 9.
To find the answer, you have list all of the possible outcomes, and if the winning combinations are squares, then 16 of 36 are correct, which if reduced, is 4 of 9
ReplyDelete-Genevieve
GRADE 7: I concluded by finding all possible combinations that the are 7 perfect squares and 9 prime numbers therefore, the totals are: 16 out of 36, 8 out of 18 or, 4 out of 9.
ReplyDeleteGRADE 8: The answer is 3 out of 36 or 1 out of 12. I looked at both possibilities and combined them. From: Luke
By doing a chart, you could find all the possibilities, which is 36
ReplyDelete1: 1,2,3,5,7,9
2: 1,2,3,5,7,9
3: 1,2,3,5,7,9
etc.
After, I had to find all the sums of each number and see what they add all up to, and then decide on which sums are prime or perfect squares. This includes:
1: 2,3,4,6,8,10
2: 3,4,5,7,9,11
3: 4,5,6,8,10,12
5: 6,7,8,10,12,14
7: 8,9,10,12,14,16
9: 10,11,12,14,16,18
Next, we have to find all the different perfect squares and prime numbers:
Prime numbers: 2,3,5,7,9,11,13,17,19
Perfect Squares: 4,9,16, 25
Numbers that are prime or perfect squares:
2,3,3,4,4,4,5,5,7,7,9,9,11,11,16,16
The fraction for this question would be 16/36 or 4/9
Here is how I went about solving the Grade 7 POTW:
ReplyDeleteIf we make a chart of some sort, we can tell that there are 36 possible outcomes. How I came up with this number is by simply doing 6 multiplied by 6 and that creates a product of 36. We can only use numbers up to 18 because that is the maximum sum that you can get from rolling both dice. But if we dig deeper into this, we find that the numbers 4, 9 and 16 appear a total of 7 times (the perfect squares). Then we also see the prime numbers are 2, 3, 5, 7, and 11. These numbers appear a total of 9 times. Then I realized that it is not possible for the sum of the digits on the two dice to be both a prime number and a perfect square. So by knowing this we can make sure that the sum has not been repeated. So we take the total amount of prime numbers (7), and the total amount of perfect squares (9), and we add them. That gives us a total of 16. Finally, to find the probability of winning we would divide 16 by 36 (the amount of possible outcomes) and we get a fraction of 4/9. When this is converted into a percentage, it is 44%. Therefore, the probability of winning on any particular roll, is 44%.
Grade 8 POTW:
ReplyDeleteI'm not actually very sure about this answer.
I think that the answer is 1/9.
I think this way because there is a 2/6 or 1/3 of rolling an odd number on the first roll, and a 4/6 or 2/3 chance of an even number.
If the number was even on the first roll, there would be a 1/6 chance of getting a 2.
I multiply it and get 1/9.
If the number was odd on the first roll, there would be a 1/3 chance of getting a 2. I multiply this and get 1/9.
So, the chance should be 1/9.
Alan
Grade 7 POTW:
ReplyDeleteI know that there are 36 possible outcomes because there are 6 numbers on each die and 6x6=36.
I made a chart to see all the possible outcomes:
1: 2,3,4,6,8,10
2: 3,4,5,7,9,11
3: 4,5,6,8,10,12
5: 6,7,8,10,12,14
7: 8,9,10,12,14,16
9: 10,11,12,14,16,18
Out of these 36 outcomes, 16 are perfect squares or prime numbers. Therefore, you would have a 16/36 or 4/9 chance of winning on any particular roll.
To find the percent of winning, you would need to divide 16 by 36 or 4 by 9 and you would get 0.4444 and so on which would round 44.5%.
The percent of winning on any particular roll is 44.5%.
Grade 8 POTW
ReplyDeleteMy answer was that the probability of the of the number on the top face being a two on the last roll is 2/9.
Grade 7 POTW:
ReplyDeleteSo first we know that there are 36 outcomes from rolling. Within these outcomes only 16 are either perfect squares or prime numbers. That means that you have a 16/36 chance or winning. Simplified to 4/9 chances of winning the game. The percentage would be 44%.
~Michelle
Grade 7 POTW #3:
ReplyDeleteFirst, we need to figure out how many possibilities there are. There are 6 numbers on each die so 6 x 6 = 36. That means there 36 possible outcomes.
Now, we make a chart so we can figure out which are perfect squares or prime numbers.
1: 2, 3, 4, 6, 8, 10
2: 3, 4, 5, 7, 9, 11
3: 4, 5, 6, 8, 10, 12
5: 6, 7, 8, 10, 12, 14
7: 8, 9, 10, 12, 14, 16
9: 10, 11, 12, 14, 16, 18
There are 4 perfect squares, which are 4, 9, 16 and 25. There are 9 prime numbers, which are 2, 3, 5, 7, 9, 11, 13, 17, 19. There are 16 prime numbers and perfect squares in total. 16 out of 36. Or 4 out of 9.
Therefore, the probability is 4/9.
Grade 7 POTW
ReplyDeleteFirst, we must find all possible outcomes, and because there is 6 numbers on each die, and there are 2 dies, 6x6=36.
To find all the prime and square numbers, I created a chart.
1:2,3,4,6,8,10
2:3,4,5,7,9,11
3:4,5,6,8,10,12
5:6,7,8,10,12,14
7:8,9,10,12,14,16
9:10,11,12,14,16,18
As you can see, there are 4 perfect squares (4,9,16,25) and 9 prime number (2,3,5,7,9,11,13,17,19). In total, there are 16 prime and square numbers.
This means that you have a 16/36 chance of winning, which is simplified to 4/9.
Therefore, the chance or probability is 4/9.
The answer is 16/36, or 4/9.
ReplyDeleteUnfortunately, my work was randomly deleted by blogger once, and then i redid it but it was deleted once again, so I did not want to redo the work again.
My method of solving this problem was to create a chart of all the possibilities, and then find the prime numbers/perfect squares in this chart.
Dhruv
My answer is 8/36, or in other words 2/9.
ReplyDeleteFirst we need to find all of the possible outcomes and then single out the answers which fit into the criteria. since there are six sides with number and 2 die, there are 36 possible outcomes (6x6=36
ReplyDelete1: 2,3,4,6,8,10
2: 3,4,5,7,9,11
3: 4,5,6,8,10,12
5: 6,7,8,10,12,14
7: 8,9,10,12,14,16
9: 10,11,12,14,16,18
IF you count there would be a total of 36 different outcomes. Now we just have to take out the prime and perfect square. There are 4 perfect squares (4,9,16 and 25) and 9 prime numbers (2,3,5,7,9,11,13,17,19). When we add those two numbers we would get 16. That means the fraction would be 16/36. This can also be changed to 4/9.
First we need to find all of the possible outcomes and then single out the answers which fit into the criteria. since there are six sides with number and 2 die, there are 36 possible outcomes (6x6=36
ReplyDelete1: 2,3,4,6,8,10
2: 3,4,5,7,9,11
3: 4,5,6,8,10,12
5: 6,7,8,10,12,14
7: 8,9,10,12,14,16
9: 10,11,12,14,16,18
IF you count there would be a total of 36 different outcomes. Now we just have to take out the prime and perfect square. There are 4 perfect squares (4,9,16 and 25) and 9 prime numbers (2,3,5,7,9,11,13,17,19). When we add those two numbers we would get 16. That means the fraction would be 16/36. This can also be changed to 4/9.
Grade 7 POTW (I was confused by perfect squares, so I just used a chart I found from the internet to help me)
ReplyDeleteI first listed out all of the possibilities! I would do a
tree diagram but I have no way to show it on technology.
1: 2,3,4,6,8,10
2: 3,4,5,7,9,11
3: 4,5,6,8,10,12
5: 6,7,8,10,12,14
7: 8,9,10,12,14,16
9: 10,11,12,14,16,18
Now we have 36 outcomes now we have to find the perfect squares and prime numbers, after using the chart to help me I figured:
4,9,16,25 are perfect squares
2,3,5,7,9,11 are the prime numbers
So there are 10 outcomes so 10/36 of winning.
After looking at other people's answers, I am left to ask, where are the 13,17 and 19 coming from?
ReplyDeleteI forgot to publish my work the first time so this one will kinda be less detailed :/
ReplyDelete1: 2,3,4,6,8,10
2: 3,4,5,7,9,11
3: 4,5,6,8,10,12
5: 6,7,8,10,12,14
7: 8,9,10,12,14,16
9: 10,11,12,14,16,18
There are 36 possibilities ^
|
Since 16 of them are perfect squares or prime numbers, we get 16/36 which when simplified is 4/9.
Mr.Milette, Vivian was unable to do the pot W on the blog because of sign in issues thus I was given the task to give you her answer of 2/9
ReplyDeleteThe answer that I got for the magic cube was 2/9. I got this by first listing the total combinations and outcomes. Basically with two different conditions there were two possible chances of cubes. 1,1,3,2,3,4 if landed on even and 2,2,6,4,6,8 if landed on odd.Also i put in the fact it is a 2/6 chance to get an odd number compared to a 4/6 chance to get an even number. With that information I was able to come up with the total combinations of rolls. 12 possible combinations were possible with odd numbers and 24 possible combinations were possible with even numbers. Thus giving me the total of 36 possibilities. With that I counted how many combinations have 2 at the end which is 8 thus giving me 8/36 which reduced is 2/9.
ReplyDeleteTo solve this potw I fist looked at the rules, if you roll an even all even numbers are halved and if you role an odd, they are all doubled, so I wrote out all of the possibility's for the first role;
ReplyDelete1: 2 6 2 4 6 8
2: 1 2 3 4 1 3
3: 2 6 2 4 6 8
4: 1 2 3 4 1 3
6: 1 2 3 4 1 3
8: 1 2 3 4 1 3
There where 36 possibility's for the first role and since the second does not count we can ignore it, out of those roles there are 8 twos so it is 8/36, but this can be made into 2/9 at the smallest, so the chance of rolling a 2 on the second roll is 2/9