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two fair dice are rolled the sum of the dice is 5

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3 Answers

This table contains all the possible sums of 2 die:
 
   | 1  2  3   4   5  6
1 | 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
 
What's the probability the sum will be 5?: 4/36 = 1/9.
 
What's the probability the sum will be >4 and <8: 15/36 = 5/12.
 
Etc.
To find the probability determine the number of successful outcomes divided by the number of possible outcomes overall. Each dice has six combinations which are independent. Therefore the number of possible outcomes will be 6*6 = 36.
 
The number of successful outcomes will be the number of outcomes where the number of the dice adds up to five. There are four successful outcomes:
 
(1)(4)
(2)(3)
(3)(2)
(4)(1)
 
 
The probability of rolling a pair of dice whose numbers add to 5 is 4/36 = 1/9.
 
Hi Erica;
Possible combinations...
1+4=5
2+3=5
3+2=5
4+1=5
Total combinations...
(6)(6)=36
 
4/36=1/9