Answer:
Hence, the probability of randomly rolling 2 standard dice and having a sum that is EVEN or GREATER THAN 9 is 2/3
Explanation:
Let A be the event that the sum of two dice is even
Then P(A) will be the probability of having even sum
As the sample space is already given in the image
n(S) = 36
A = {(1,1) , (1,3), (1,5), (2,2), (2,4), (2,6), (3,1), (3,3), (3,5), (4,2), (4,4), (4,6), (5,1), (5,3), (5,5), (6,2), (6,4), (6,6)}
n(A) = 18
So,
P(A) = n(A)/n(S)
= 18/36
= 1/2
Let B be the event that the sum is greater than 9
B = {(4,6), (5,5), (5,6), (6,4), (6,5), (6,6)}
n(B) = 6
P(B) = n(B)/n(S)
= 6/36
= 1/6
Now we have to find P(A∪B) i.e. P(A or B)
P(A∪B) = P(A) + P(B)
= 1/2 + 1/6
= (3+1)/6
=4/6
=2/3
Hence, the probability of randomly rolling 2 standard dice and having a sum that is EVEN or GREATER THAN 9 is 2/3 ..