An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events.

Event A: The sum is greater than 6.
Event B: The sum is not divisible by 5 and not divisible by 6.

Round your answers to TWO decimal places.

The sample space of rolling two dice has 36 possible outcomes.  Remember that the "sample space" is a set which contains all possible outcomes.   

(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)

(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)

(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)

(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)

(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)

(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)

The probability of rolling a 2 is 1/36.

The probability of rolling a 3 is 2/36.

The probability of rolling a 4 is 3/36.

The probability of rolling a 5 is 4/36.

The probability of rolling a 6 is 5/36. 

The probability of rolling a 7 is 6/36.

The probability of rolling an 8 is 5/36.

The probability of rolling a 9 is 4/36.

The probability of rolling a 10 is 3/36.

The probability of rolling an 11 is 2/36.

The probability of rolling a 12 is 1/36.

Using these probabilities, you can answer your questions:

Probability of rolling a number bigger than 7 is the sum of the probabilities of rolling an 8, 9, 10, 11, and 12.

5/36 + 4/36 + 3/36 + 2/36 + 1/36 = 15/36 which reduces to 5/12

Probability of rolling a number divisible by 4 is the sum of the probabilities of rolling a 4, 8, and 12.

3/36 + 5/36 + 1/36 = 9/36 which reduces to 1/4.

Hope this helps.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.