if you tossed two number cubes, what sum has the greatest probability of occuring? Explain.
7 because it is the number which is the nearest number to the middle.
(0.5 meant add 1)
a sum of 7 has a prob of 6/36 = 1/6
to get a 7:
16, 25, 34, 43, 52, 61 ----> 6 of them
all other sums have a lesser count
e.g.
to get a 5:
14, 23, 32, 41, --- only 4 of them
well this is no help at all so take this website down now
Look at the list. 7 is in all of the lists, so 7 is the answer.
1,1=2
1,2=3
1,3=4
1,4=5
1,5=6
1,6=7
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2,1=3
2,2=4
2,3=5
2,4=6
2,5=7
2,6=8
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3,1=4
3,2=5
3,3=6
3,4=7
3,5=8
3,6=9
-----------------------------------------
4,1=5
4,2=6
4,3=7
4,4=8
4,5=9
4,6=10
-----------------------------------------
5,1=6
5,2=7
5,3=8
5,4=9
5,5=10
5,6=11
--------------------------------------------
6,1=7
6,2=8
6,3=9
6,4=10
6,5=11
6,6=12
That's correct! Another way to explain it is that there are 6 different ways to get a sum of 7 when tossing two number cubes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1), which is more than any other possible sum. Therefore, the sum of 7 has the greatest probability of occurring.
To determine the sum that has the greatest probability of occurring when two number cubes are tossed, we need to analyze the possible outcomes and count the number of times each sum occurs.
A number cube has six sides, numbered from 1 to 6. When two number cubes are tossed, the sum of the numbers on the top faces can be any value between 2 (when both cubes show a 1) and 12 (when both cubes show a 6).
To find the probability of each sum occurring, we can create a table or a chart with all the possible outcomes:
Sum | Possible Outcomes
---|---
2 | (1,1)
3 | (1,2), (2,1)
4 | (1,3), (2,2), (3,1)
5 | (1,4), (2,3), (3,2), (4,1)
6 | (1,5), (2,4), (3,3), (4,2), (5,1)
7 | (1,6), (2,5), (3,4), (4,3), (5,2), (6,1)
8 | (2,6), (3,5), (4,4), (5,3), (6,2)
9 | (3,6), (4,5), (5,4), (6,3)
10 | (4,6), (5,5), (6,4)
11 | (5,6), (6,5)
12 | (6,6)
Now we can count the number of outcomes for each sum:
Sum | Number of Outcomes
---|---
2 | 1
3 | 2
4 | 3
5 | 4
6 | 5
7 | 6
8 | 5
9 | 4
10 | 3
11 | 2
12 | 1
From the table, we can see that the sums 6 and 8 have the highest probability of occurring, with a count of 5 each. Therefore, the sums 6 and 8 have the greatest probability of occurring when two number cubes are tossed.
It is worth mentioning that in this case, since the number cubes are fair and unbiased, each outcome has an equal probability of occurring. However, the sums 6 and 8 have more possible outcomes, which is why they have a greater probability of occurring compared to the other sums.