What is the probability of getting a sum of either 7, 11, or 12 on a roll of two dice?
2 Answers
The probability is
Explanation:
Let's first take a look at the probability for one of those sums.
There are
(1,1), (1,2), ..., (1, 6)
(2, 1), (2, 2), ..., (2,6)
...
(6,1), (6,2), ..., (6,6)
The probability of each one of those is
- How many possible combinations of two dice will give you a sum of
7 ? There are6 combinations:(1,6) ,(6,1) ,(2,5) ,(5,2) ,(3,4) and(4,3) .
=> P("sum"=7) = 6 * 1/36 = 6/36 = 1/6
- For a sum of
11 , there are2 combinations:(5,6) and(6,5) .
=> P("sum"=11) = 2 * 1/36 = 2/36 = 1/18
- For a sum of
12 , there is just1 combinations:(6,6) .
=> P("sum"=12) = 1/36
Now, how do you combine those three probabilities?
The events "
For independent events
P(A " or " B) = P(A) + P(B)
Thus, our probability is
P = P("sum"=7) + P("sum"=11) + P("sum"=12)
= 6/36 + 2/36 + 1/36 = 9/36
= 1/4
= 25%
Explanation:
You can draw up a possibility space and count how many of the outcomes meet the requirements.
The following array shows the sum of two dice thrown.
(Created by Parzival)
{: (color(white)(0)," "ul1" "," "ul2" "," "ul3" "," "ul4" "," "ul5" "," "ul6" "),(1|," "2" "," "3" "," "4" "," "5" "," "6" "," "color(red)(7)" "),(2|," "3" "," "4" "," "5" "," "6" "," "color(red)(7)" "," "8" "),(3|," "4" "," "5" "," "6" "," "color(red)(7)" "," "8" "," "9" "),(4|," "5" "," "6" "," "color(red)(7)" "," "8" "," "9" "," "10" "),(5|," "6" "," "color(red)(7)" "," "8" "," "9" "," "10" "," "color(red)(11)" "),(6|," "color(red)(7)" "," "8" "," "9" "," "10" "," "color(red)(11)" "," "color(red)(12)" ") :}
There are
Of these there are
