dice myp assignment

Aastha Pandey MYP Assignment: DICE

DiceQuestion 1

Dice 1 2 3 4 5 61 2 3 4 5 6 7

2 3 4 5 6 7 8

3 4 5 6 7 8 9

4 5 6 7 8 9 10

5 6 7 8 9 10 11

6 7 8 9 10 11 12

Question 2

We can get 4 three times. When you roll the dice and get 2 and 2, and when you roll the dice and get 3 and 1. So the probability of getting a 4 is 3 out of 36. Which is 1 out of 12.

Question 3

(Probability = )

Divisible by 4: The probability of getting a number that is divisible by 4 is . The reason why it is, is because there are 3 numbers that are divisible by 4, they are: 4, 8, and 12. However, 4 appears three times, 8 appears five times and 12 appears one time. Therefore, there are 9 outcomes that are divisible

by four. So the answer should be that simplifies to .

Divisible by 2: The probability of getting a number that is divisible by 2 is . The reason why it is, is because there are five numbers that are divisible by 2, they are: 4, 6, 8, 10, and 12. However, 4 appears three times, 6 appears five times, 8 appears five times, 10 appears 3 time, and 12 appears one time.

Therefore, there are 17 outcomes. So the answer should be .


Divisible by 3: The probability of getting a number that is divisible by 3 is . The reason why it is, is because there are three numbers that are divisible by 3, they are: 6, 9 and 12. However, 6 appears 5 times, 9 appears 4 times and 12 appears one time. Therefore, there are 10 outcomes. So the answer should be

that simplifies to .

Divisible by 6: The probability of getting a number that is divisible by 6 is . The reason why it is, is because there is only one number that is divisible by 6, it is: 12. Also, it appears only once on the table, therefore, there is only one

outcome. So the answer is .

Explain: For these questions the way I calculated it was very simple. If a number is “divisible by” then you can just think of their multiples. So I just counted how many whole numbers on the table can divide the number on the question and will get a 0.

Question 4:

Looking at the answers in question 3, a pattern could be found. First of all, to find the numbers all I had to check was that the outcomes can divide the numbers and get a result of 0 at the end.

To find the answers for 4, all that was needed to be done was multiplied by an outcome. If the answer is a whole number then it is divisible. This was the same for all three other numbers, with 2, 3, and 6.

So the final formula for this is . However, this formula doesn’t always apply to all the numbers, the final outcome has to be a factor of 36 to be used in this formula. Also, the range of the final outcome needs to 1 < n < 12 (greater than one and smaller than twelve).

Examples to prove this would be:

Example proving it False:

Finding the probability of a number that is divisible by 9: The probability is 0 because there are no multiples of 9 in the table. So this is proved False.


Finding the probability of a number that is divisible by 7: The probability is 0 because there are no multiples of 7 in the table. So this is proved False.

An example proving is True:

Finding the probability of a number that is divisible by 5: The probability is because the outcome that is divisible by 5 is 10, and there are three 10s in the

table which is: , which simplifies to .

Question 5:

Outcome Number of outcome

Probability

3 1

4 3

5 6

6 10

7 15

8 21

9 25

10 27

11 27

12 25

13 21

14 15

15 10

16 6


17 3

18 1

SUM 216 1

My conjecture is valid for the three dice experiment as well, because as long

as a number turns out to be a whole number after multiplied by and is 1 < n < 216 (greater than one and smaller than 216).

An example proving it True:Finding the probability of a number that is divisible by 8: The probability of

getting a number divisible by 8 is because there is one outcome overall that is divisible by 8, which is sixteen. Also, there are six sixteen’s so the probability is

which then simplifies to .

This conjecture is valid, but at the same time may be invalid because some of the numbers don’t have other outcomes that can be divided with.

An example proving it False:Finding the probability of a number that is divisible by 10: The probability is 0 because this number is too large for the chart, and there aren’t any other outcomes, in this table that is divisible by ten.

dice myp assignment

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