Thursday, September 17, 2015
Math POTW #3 - Keep Up the Great Work!
Great work on the last POTW everyone. It was great to see the different ways to solve the elaborate word problem (I saw mostly algebraic and Guess and Check strategies used). I also loved seeing such full detail in your explanations. My next challenge for your POTW responses is to REPLY and post COMMENTS/QUESTIONS to your peers' POTW responses/answers. The latest POTW is found below:
Subscribe to:
Post Comments (Atom)
My solution was that there is a 1/3 chance to get an odd sum and win the game.
ReplyDeleteTo solve this problem, I found all of the possible combinations:
1+2+3
1+2+4
1+2+5
1+3+4
1+3+5
1+4+5
Then, I found the sums and labeled which ones were odd, and which were even.
1+2+3=6 - even
1+2+4=7 - odd
1+2+5=8 - even
1+3+4=8 - even
1+3+5=9 - odd
1+4+5=10 - even
Two of the six (2/6) sums were odd, and four of the six (4/6) sums were even.
Since to win, the player needed an odd sum, I focused on the number of odd sums that I had found.
2/6 can be reduced to 1/3 (by dividing both the numerator and denominator by 2).
Therefore, the player has a 1/3 chance to get an odd sum and win the game.
There are 5 balls in the bag and 10 possibilities
ReplyDelete3/5 of the balls are odd and the other 2/5 are even
1+3=4 which is even
1+5=6 which also is an even number
1+2=3 which is odd so, so far 1/10 possibilities that are odd
1+4=5 which is also odd so now there are 2/10 possibilities that are odd
3+5=8 which is even
3+2=5 which is odd so now there are 3/10 odd possibilities
3+4=7 which is also odd, now there are 4/10 odd possibilities
5+2=7 also, so there are now 5/10 odd possibilities
5+4=9, also an odd number the odd possibilities are at 6/10
Finally, 2+4=6 which i even
Therefore, the final probability of the player winning the game is 6/10 or 3/5
Here is how I answered the question:
ReplyDeleteFirst I figure out all possible outcomes by make a tree of possibilities;(/=or)
1-2-3/4/5/ 2-1-3/4/5/ 3-1-2/4/5/ 4-1-2/3/5/ 5-1-2/3/4/
1-3-2/4/5/ 2-3-1/4/5/ 3-2-1/4/5/ 4-2-1/3/5/ 5-2-1/3/4/
1-4-2/3/5/ 2-4-1/3/5/ 3-4-1/2/5/ 4-3-1/2/5/ 5-3-1/2/4/
1-5-2/3/4/ 2-5-1/3/4/ 3-5-1/2/4/ 4-5-1/2/3/ 5-4-1/2/3/
Each number can have 4 different second numbers and 3 different third numbers which is 3 times 4 to find how many possible combinations can one number lead to which is 12. I multiply 12 by 5 for the five possible first number pulls, which is 60. There are 60 possible combinations.
Let's find the sums now:
1+2+3=6 / 1+2+4=7 / 1+2+5=8 / 1+3+2=6 / 1+3+4=7 / 1+3+5=8 / 1+4+2=7 / 1+4+3=8 / 1+4+5=10 / 1+5+2=8 / 1+5+3=9 / 1+5+4=10 / 2+1+3=6 / 2+1+4=7 / 2+1+5=8 / 2+3+4=9 / 2+3+1=6 / 2+3+5=10 / 2+4+1=7 / 2+4+3=9 / 2+4+5=11 / 2+5+1=8 / 2+5+3=10 / 2+5+4=11 / 3+1+2=6 / 3+1+4=8 / 3+1+5=9 / 3+2+1=6 / 3+2+4=9 / 3+2+5=10 / 3+4+1=8 / 3+4+2=9 / 3+4+5=12 / 3+5+1=9 / 3+5+2=10 / 3+5+4=12 / 4+1+2=7 / 4+1+3=8 / 4+1+5=10 / 4+2+1=7 / 4+2+3=9 / 4+2+5=11 / 4+3+1=8 / 4+3+2=9 / 4+3+5=12 / 4+5+1=10 / 4+5+2=11 / 4+5+3=12 / 5+1+2=8 / 5+1+3=9 / 5+1+4=10 / 5+2+1=8 / 5+2+3=10 / 5+2+4=11 / 5+3+1=9 / 5+3+2=10 / 5+3+4=12 / 5+4+1=10/ 5+4+2=11 / 5+4+3=12
There is: Even numbers Odd numbers
-6 sixs -6 sixs -7 sevens
-7 sevens -12 eights -11 nines
-12 eights -12 tens -6 elvens
-11 nines -6 twelves 24 total out of 60
-12 tens -36 total out of 60
-6 elvens
-6 twelves
- 60 total
So the probability of getting an odd number after adding the three numbers is 24/60 while getting an even number has a probability of 36/60 so the probability of that player winning the game is 24/60 or unlikely. (Sorry for all the numbers it is just to show how I did it, Which was the long way of doing it and there is probably a shorter method but I decided to do it this way so I can be sure plus I’m very patient when it comes to solving a math problem)
The smallest fraction of the probabilty is 2/5.
Deletethe reason why I found 60 answers is because I included possible outcomes with the same numbers just a different order which I believe would not effect the answers as Seyone found the same answer with only 10 possible outcomes
DeleteI made a chart to find the total amount of chances. I found out there are only 10 different outcomes, as the order in which the balls are picked don't matter and aren't included. Without repeating any, there are only 10. Then, I added each one individually to see whether it was odd or even, and found only 4/10, which were 1,2,4 (7), 1,3,5, (9), 2,3,4(9), 2,4,5(11). So the probability of picking a odd sum is 4/10, or 2/5 reduced.
ReplyDeleteI got the same answer I just included all the possible outcomes because I decided to do it the hard way.
DeleteI agree with Seyone since the order in which the balls are picked has no effect on the sum
DeleteSame here, if I wrote every possible outcome including which order the balls were chosen on, I´d still get the same answer, just less efficient and more difficult. I have to discard every outcome that had already been done, which would trip me out, and I would end up with a lot of duplicates because I got confused. Also it´s just not necessary because like you guys have said, the order has no effect on the sum
DeleteI found 10 possible outcomes. I was limited to only adding 3 numbers since the player had to pick 3 balls. I also couldn't have equations with two of the same number in it since there were only 5 balls numbered from 1-5. I also didn't take to account which order the balls were picked in, since you would win the game if the sum of the three numbers was an odd number, it didn't matter whether a one was picked first or last. So here are the 10 possible outcomes:
ReplyDelete1+2+3=6 1+4+5=10
1+2+4=7 2+3+4=9
1+2+5=8 2+3+5=10
1+3+4=8 2+4+5=11
1+3+5=9 3+4+5=12
So out of all the 10 outcomes, only 4 were odd (1+2+4, 1+3+5, 2+3+4, 2+4+5) meaning the player has a 4/10 chance of winning, or a 2/5 chance when reduced.
First I made a list of all the possible outcomes...
ReplyDelete1,2,3- even
1,2,4- odd
1,2,5- even
1,3,4- even
1,3,5- odd
1,4,5- even
2,3,4- odd
2,3,5- even
2,4,5- odd
3,4,5- even
I found 10 possible outcomes.
Of those 10 outcomes 4 had odd sums.
Therefore the probobility of winning (drawing an odd number) is 4/10 or as a reduced fraction 2/5.
I realized that I forgot a few possible combinations in my previous post, so I fixed my work below:
ReplyDeleteMy solution was that there is a 2/5 chance to get an odd sum and win the game.
To solve this problem, I found all of the possible combinations:
1+2+3
1+2+4
1+2+5
1+3+4
1+3+5
1+4+5
2+3+4
2+3+5
2+4+5
3+4+5
Then, I found the sums and labeled which ones were odd, and which were even.
1+2+3=6 - even
1+2+4=7 - odd
1+2+5=8 - even
1+3+4=8 - even
1+3+5=9 - odd
1+4+5=10 - even
2+3+4=9 -odd
2+3+5=10 -even
2+4+5=11 -odd
3+4+5=12 -even
4 of the 10 (4/10) sums were odd, and 6 of the 10 (6/10) sums were even.
Since to win, the player needed an odd sum, I focused on the number of odd sums that I had found.
4/10 can be reduced to 2/5 by dividing both the numerator and denominator by 2.
Therefore, the player has a 2/5 chance to get an odd sum and win the game.
First, I read the question and noticed that when u pick the three balls they all have to be different because there are only 5 number from 1-5. For instance if you pick 1 on your first try, 3 on your second try, you can't pick either 1 or 3 on your third try because 1 and 3 aren't in the bag anymore.
ReplyDeleteNext, I listed out all the different outcomes:
1+2+3=6-even
1+2+4=7-odd
1+2+5=8-even
1+3+4=8-even
1+3+5=9-odd
1+4+5=10-even
2+3+4=9-odd
2+3+5=10-even
2+4+5=11-odd
3+4+5=12-even
There are a total of 10 outcomes in total and out of that 4 are odd while 6 are even. Therefore, the chance of winning this game is 4/10 or 2/5 in reduced form.
To solve this problem, first I made a list of the 10 possible outcomes:
ReplyDelete1+2+3=6=even
1+2+4=7=odd
1+2+5=8=even
1+3+4=8=even
1+3+5=9=odd
1+4+5=10=even
2+3+4=9=odd
2+3+5=10=even
2+4+5=11=odd
3+4+5=12=even
Of the 10 possible outcomes 6 are even, whereas 4 are odd. Therefore, the fraction of winning this game would be 4/10 or 2/5 (reduced).
Since you can't get a number twice, there is never the same combination more than once. That means that there won't be too many sums and I could find them all.
ReplyDeleteThese are all of the combinations and sums:
1+2+3=6
1+2+4=7
1+2+5=8
1+3+4=8
1+3+5=9
1+4+5=10
2+3+4=9
2+3+5=10
2+4+5=11
3+4+5=12
The chance of winning the game is 2/5 (4/10 reduced), since there are a total of ten sums and 4 of them are odd. I also know from my background knowledge that there are more ways to get even sums than odd sums, so I think I am correct.
First of all, I wrote down every combination that could be drawn from the bag. There are 5 number, 3 odd and 2 even, no repeats.
ReplyDeleteOnce a number is drawn it could not be drawn again.
Those were the preliminaries.
I figured out that an odd number is the sum of either, 2 even numbers and 1 odd or 3 odd numbers.
o= odd e= even
123- e 124=o
125=e 134=e
135=o 145=e
234=o 235=e
245=o 345=e
In the end, 4/10 of all possible combinations were odd. So therefore, the simplified 2/5 is the possibility of getting an odd sum and winning.
The first thing I did was list the two opposite extremes 3,4,5 (in any order) and 1,2,3 (in any order) 3+4+5 = 12. 1+2+3=6. Then I take away 12 by 6 to give me the possibilities for the sums. 12-6=6. After that, I figured out with some common sense that 3, 4, 5 can be arranged in 6 amount of ways. 3, 4 ,5| 3, 5, 4| 4,5,3| 4,3,5| 5,3,4| 5,4,3. This means that I can get to any possibility in 3 ways. So I multiply 6 ( my difference) by the 6 possibilities per number to get me 36 possibilities. 6x6=36. Then, i listed the answers/possibilities/outcomes. 6,7,8,9,10,11,12. 7,9,and 11 are the odd numbers. 6,8,10, and 12 are the even numbers. There are 3 odd numbers and 4 even numbers. 3 + 4 = 7. 7 is the denominator. Since the odd numbered outcomes are what a player needs to win, the total of odd numbered outcomes is the numerator. 3/7. Since 7 is a prime number, it is impossible to find any smaller of a fraction.
ReplyDeleteThere are 10 possible combinations
ReplyDelete1+2+3=6 even
1+2+4=7 odd
1+2+5=8 even
1+3+4=8 even
1+3+5=9 odd
1+4+5=10 even
2+3+4=9 odd
2+3+5=10 even
2+4+5=11 odd
3+4+5=12 even
This shows that 4/10 of the possibilities are odd. (2/5 reduced)
To solve this question, I first made all of the possible combinations that could be made from the 5 balls:
ReplyDelete1+2+3=6 (even)
1+2+4=7 (odd)
1+2+5=8 (even)
1+2+6=9 (odd)
1+4+5=10 (even)
2+3+4=9 (odd)
2+3+5=10 (even)
2+4+5=11 (odd)
3+4+5=12 (even)
6/10 are even, and 4/10 are odd.
The probability of getting odd possibilities is 2/5
So first I found all the possible combinations, the sums and then I wrote if the sums were odd or even.
ReplyDelete1+2+3= 6 (even)
1+2+4= 7 (odd)
1+2+5= 8 (even)
1+3+4= 8 (even)
1+3+5= 9 (odd)
1+4+5= 10 (even)
2+3+4= 9 (odd)
2+3+5= 10 (even)
2+4+5= 11 (odd)
3+4+5= 12 (even)
Then I counted the possibilities- there were 10. I then counted the even and odd sums. There were 6 even sums, and 4 odd sums. So there was a 4/10 chance to win the game, or 2/5 reduced.
To answer the question first I found the possilible out comes,and with out any repeats there are 10 possibilities, even possibilities being, 1 2 3=6, 1 2 5=8, 1 3 4=8, 1 4 5=10, 2 3 5=10 and 3 4 5=12, and the odd possibilities being, 1 2 4=7, 1 3 5=9, 2 3 4=9, and 2 4 5=11, which is 6 even outcomes and 4 odd outcomes so the probability of a player winning is 4/10, and the probability of losing is 6/10.
ReplyDeleteThere are 10 possible outcomes
ReplyDeleteOdd= (O)
Even=(E)
1+2+3=6 (E)
1+2+4=7 (O)
1+2+5=8 (E)
1+3+4=8 (E)
1+3+5=9 (O)
1+4+5=10 (E)
2+3+4=9 (O)
2+3+5=10 (E)
2+4+5=11 (O)
3+4+5=12 (E)
4 of the sums are odd
6 of the sums are even
So the chance of winning this game is 4/10 or 2/5
The chance of losing this game is 6/10 or 3/5
This comment has been removed by the author.
ReplyDeleteFirst I found all the possibilities and the sums and labeled the odds and evens, then I counted the amount of odds and evens:
ReplyDelete1 + 2 + 3 = 6 E
1 + 2 + 4 = 7 O
1 + 2 + 5 = 8 E
1 + 3 + 4 = 8 E
1 + 3 + 5 = 9 O
1 + 4 + 5 = 10 E
2 + 3 + 4 = 9 O
2 + 3 + 5 = 10 E
2 + 4 + 5 = 11 O
3 + 4 +5 = 12 E
Since there were 10 possibilities and 4 were odd, there is a 4/10 chance that the player will win or 2/5 chance the player will win.
My answer to this question was to simply make a tree graph to represent this question.
ReplyDeleteHere are the outcomes:
1+2+3
1+2+4
1+2+5
1+3+4
1+3+5
1+4+5
2+3+4
2+3+5
2+4+5
3+4+5
Basically as I counted it was clear that there are ten different possibilities. In those ten possibilities I found that six of them were even numbers. (6,8,8,10,10,12) Then I found that there were 4 odd numbers. (7,9,9,11) Thus giving me the answer that there is a 4/10 chance to win. (or 2/5 if reduced)
Answer
ReplyDelete123=6
124=7
125=8
134=8
135=9
145=10
234=9
235=10
245=11
354=12
ten possible outcomes
4 odd numbers
the chances of pulling out an odd combo is 4/10 or 2/5
40% is the percentage
To solve this problem, I made a list of all the possible combinations (in the numbers 1-5) and their outcomes:
ReplyDelete1+2+3=6 (Even)
1+2+4=7 (Odd)
1+2+5=8 (Even)
1+3+4=8 (Even)
2+3+4=9 (Odd)
1+3+5=9 (Odd)
1+4+5=10 (Even)
2+3+5=10 (Even)
2+4+5=11 (Odd)
3+4+5=12 (Even)
Out of all the possible outcomes, 6 are even and 4 are odd, so the chances of someone winning is ⅖ (4/10), 40%, or 0.4. The probability that someone loses is ⅗ (6/10), 60%, or 0.6. The probability of someone losing is greater than that of winning.
To solve this problem I decided to make a tree graph to represent the different outcomes and to see which are odd and which are even. The table looked like this:
ReplyDelete1+2+3(Even)
1+2+4(Odd)
1+2+5(Even)
1+3+4(Even)
1+3+5(Odd)
1+4+5(Even)
2+3+4(Odd)
2+3+5(Even)
2+4+5(Odd)
3+4+5(Even)
After completing my tree graph I found that there was a total of 10 different possible outcomes with 6 of them being even and 4 of them being odd. The even sums were 6,8,8,10,10,12 and the odd sums were 7,9,9,11. Therefor there is a 4/10 chance to win this game or 2/5 if we reduce it.
All the possible sum outcomes:
ReplyDelete1+4+5=10
1+3+5=9
1+2+5=8
2+4+5=11
2+3+5=10
3+4+5=12
1+3+4=8
1+2+4=7
2+3+4=9
1+2+3=6
The probability of getting a odd sum, and winning the game is 1/4
The answer I found was 4/10 or 2/5. I found this by listing all possible outcomes. The possibilities include: 1+2+3= 6, 1+2+4=7, 1+2+5= 8, 1+3+4= 8, 1+3+5=9, 1+4+5= 10, 2+3+4=9, 2+4+5=11, 2+3+5= 10, 3+4+5= 12. Then I counted the amount of sums that were odd which was 4 out of the 10 possibilities. Therefore the chances of winning this game is 4/10 or 2/5.
ReplyDeleteThe chance of winning the game is ⅖ chances.
ReplyDeleteHow I got this answer was that I first listed all the possible outcomes you can get when drawing 3 balls from the bag.
1+2+3 = 6
1+2+4 = 7
1+2+5 = 8
1+3+4 = 8
1+3+5 = 9
2+3+4 = 9
1+4+5 = 10
2+3+5 = 10
2+4+5 = 11
3+4+5 = 12
Then I counted the odd sums from my addition, which was 7, 9, 9, and 11. These were the only outcomes that were odd and there were four of them. Then I counted how many possibilities there were altogether in order to get the denominator of the fraction. There were ten possibilities so I made than the denominator of my fraction which is now 4/10. But since you always want to know the lowest fraction you want to reduce it to ⅖ by dividing the numerator and the denominator by 2.
In conclusion the answer that I got for this question is ⅖.
To start the question I first decided to find all possibilities that you could obtain by picking out 3 out of the numbers 1,2,3,4,5,
ReplyDeleteThe possibilities are as followed
1,2,3= 6 Even
1,2,4= 7 Odd
1,2,5= 8 Even
1,3,4= 8 Even
1,3,5= 9 Odd
1,4,5= 10 Even
2,3,4= 9 Odd
2,3,5= 10 Even
3,4,5= 12 Even
2,4,5= 11 Odd
As you can see, there is a total of 10 possibilities with 4 of the possibilities resulting in a sum of a odd number. This means there is a 4/10 chance of winning this game. If reduced the answer is probability of 2/5 with the percentage of winning being 40%
Wow, congrats to the numerous students who obtained the correct answer of 4/10 (2/5) or 40% chance. If you did not obtain that answer, please have a look at some of your peers' work and see where you may have gone astray. If you are still stuck, please see me and I can review the correct process.
ReplyDeleteRegardless of right or wrong, there was some great work done here. Keep it up on POTW#4!
I think where I went wrong was counting the possibilities. it took many cornerstones by thinking that the way they are picked up is a different way to get the same answer, therefore more answers for the same one. I also forgot that there are other numbers added together can equal the same thing, therefore shortening it.
ReplyDeleteIt was actually 1+2+3= 6 even
1+2+4= 7 is a odd number 1+2+5= 8 is a even number even 1+3+4= 8 is a even 1+3+5= 9 is a odd number 1+4+5= 10 is a even number 2+3+4= 9 is a odd number 2+3+5= 10 is a even number 3+4+5= 12 is a even number 2+4+5= 11 is a odd.
Therefore, the probability of getting a odd number is 4/10.