Jill made two 6 sided dice and labeled each of them with these numbers.
-3, -2, -1, 0, 1, 2
Suppose this pair of dice was tossed 1,000 times and the numbers on the two top faces were added. Which sum would probably be the most common? And why?
Draw a 6 by 6 matrix containing the given numbers in the rows and columns
Fill in the sums , just like you would for the numbers from 1 to 6 in a regular die.
Which sum is the most common?
How many times out the 36 sums does it appear?
find the probability.
multiply that probability by 1000
Due tomorrow and I still don't get
To determine the most common sum when the two dice are tossed, we need to consider the possible combinations of the top faces of the two dice and calculate the frequency of each sum occurring.
First, let's list all the possible combinations of the top faces of the two dice and their corresponding sums:
-3 -3 = -6
-3 -2 = -5
-3 -1 = -4
-3 0 = -3
-3 1 = -2
-3 2 = -1
-2 -3 = -5
-2 -2 = -4
-2 -1 = -3
-2 0 = -2
-2 1 = -1
-2 2 = 0
-1 -3 = -4
-1 -2 = -3
-1 -1 = -2
-1 0 = -1
-1 1 = 0
-1 2 = 1
0 -3 = -3
0 -2 = -2
0 -1 = -1
0 0 = 0
0 1 = 1
0 2 = 2
1 -3 = -2
1 -2 = -1
1 -1 = 0
1 0 = 1
1 1 = 2
1 2 = 3
2 -3 = -1
2 -2 = 0
2 -1 = 1
2 0 = 2
2 1 = 3
2 2 = 4
Next, we count the frequency of occurrence for each sum:
-6: 1
-5: 2
-4: 3
-3: 4
-2: 5
-1: 6
0: 7
1: 6
2: 5
3: 4
4: 3
From the counts, we can observe that the sum 0 occurs the most frequently, with a count of 7. Therefore, the most common sum when the two dice are tossed is 0.
The reason why 0 is the most common sum is because it can be obtained in more ways (7 out of 36 possible combinations) compared to other sums. This is because when the numbers on the top faces of the dice are symmetrically balanced around 0 (with -3 and 3 as the outliers), more combinations lead to a sum of 0.
Note: It is important to calculate the probabilities and frequencies mathematically to obtain an accurate answer.