SOLUTION: Suppose a pair of fair dice is rolled once. Find the probability of rolling:
what is the posibility that it is A sum of 8 or greater
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Probability-and-statistics
-> SOLUTION: Suppose a pair of fair dice is rolled once. Find the probability of rolling:
what is the posibility that it is A sum of 8 or greater
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The values on each die are 1 through 6. We can make a chart as shown below
Each number in black is a sum of the red and blue dice. Eg: add the blue 2 to the red 4 and you get 2+4 = 6 which is shown in row 2, column 4.
The chart shows all the ways to add two values on six-sided dice.
There are 6 rows and 6 columns leading to 6*6 = 36 sums overall.
Of these 36 values, we only care about the ones highlighted with various colors
Sums of 8 marked in yellow. There are 5 such cells.
Sums of 9 marked in blue. There are 4 such cells.
Sums of 10 marked in pink. There are 3 of them.
Sums of 11 marked in green. There are 2 green cells.
Sums of 12 marked in gray. There is only 1 way to roll a 12.
Add up all those counts: 5+4+3+2+1 = 15
So there are 15 cells highlighted with a color
Meaning there are 15 ways to get what we want (a sum of 8 or higher)
This is out of 36 ways total
The probability of rolling an 8 or higher is 15/36 = (3*5)/(3*12) = 5/12
Using a calculator, we get 5/12 = 0.4167 approximately which converts to 41.67% after you move the decimal point 2 spots to the right.
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In summary,
Answer in fraction form: 5/12
Answer in decimal form: 0.4167 (approximate)
Answer in percent form: 41.67% (approximate)
The three different answers are saying the same basic thing, but in a slightly different way.
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