Answer: [tex]c.\ \dfrac{5}{9}[/tex]
Step-by-step explanation:
The total number of outcomes of rolling a die =6
Then , the total number of outcomes of rolling two dice = 6 x 6 = 36
Now , Pairs of outcomes having a sum that is EVEN = (1,1), (2,2), (3,3) , (4,4), (5,5), (6,6) , (1,3), (1,5), (2,4), (2,6), (3,1), (3,5), (4,2), (2,6),(5,3), (5,1), (6,4), (6,2)
i.e. Number of outcomes having a sum that is EVEN = 18
Pairs of outcomes having a sum that is GREATER THAN 9 = (4,6), (6,4), (5,5), (5,6), (6,5), (6,6)
i.e. Number of outcomes having a sum that is GREATER THAN 9 =6
Number of outcomes having a sum that is EVEN and GREATER THAN 9 ((4,6), (6,4), (5,5), (6,6)) = 4
Now , the Number of outcomes having a sum that is EVEN or GREATER THAN 9 = (Number of outcomes having EVEN sum)+(Number of outcomes having sum GREATER THAN 9 )-(Number of outcomes having a sum EVEN and GREATER THAN 9 )
= 18+6-4=20
Now , the probability of randomly rolling 2 standard dice and having a sum that is EVEN or GREATER THAN 9 = [tex]\dfrac{\text{Number of rollings having a sum that is EVEN or GREATER THAN 9 }}{\text{Total outcomes}}\\\\=\dfrac{20}{36}=\dfrac{5}{9}[/tex]
Hence, the correct answer is [tex]c.\ \dfrac{5}{9}[/tex]
