Option C:
[tex]\frac{7}{36}[/tex]
Solution:
Sample space for two dice
[tex]=\left\{\begin{array}{l}{(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)} \\{(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)} \\{(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)} \\{(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)} \\{(5,1),(5,2),(5,3),(5,4),(5,5),(6,6)} \\{(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}\end{array}\right.[/tex]
Number of sample space = 36
Pair getting sum of 12 = (6, 6)
Number of pair getting sum of 12 = 1
Pair getting doublet = (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)
Number of pair getting doublet = 6
Total number of pair getting sum of 12 or doublet = 1 + 6 = 7
Probability of getting sum of 12 or doublet
[tex]= \frac{\text { Total number of getting sum of } 12 \text { or doublet }}{\text { Number of sample space }}[/tex]
[tex]=\frac{7}{36}[/tex]
Hence, [tex]\frac{7}{36}[/tex] is the probability of getting a sum of 12 or doublet when rolling a pair of dice.
