Question

Two dice are rolled. Determine the probability of the following. (Enter your probabilities as fractions.)(a) rolling an even sum _____(b) rolling a sum greater than 7 ______(c) rolling an even sum and a sum greater than 7 ______(d) rolling an even sum or a sum greater than 7 ______

Answer 1

First, we need to find the sample space for two dice. Since each dice has 6 faces, the sample space is

which consist in 36 elements.

Part A.

In this case, we need to find the combinations where the sum of the 2 dice is even. The combinations are:

for instance, in the upper left corner, the sum is 1+1=2, which is an even number and similarly for the other cases.

As we can note, there are 18 possible combinations. Then, the probability is

`P(\text{ even sum)=}(18)/(36)=(1)/(2)`

Part B.

In this case, we need to find the possible combinations where the sum of the 2 dices is greater than 7. The possible combinations are:

Since there are 15 possible combinations, the probability is given by

`P(\text{ Sum greater than 7)=}(15)/(36)`

Part C.

This case is the intersection of the two cases from above. The possible combinations are:

Since there are 9 possible combinations, the probability is

`P(\text{Even sum and sum greater than 7)=}(9)/(36)=(1)/(4)`

Part D.

We need to find the possible combinations where the sum is even or the sum is greater than 7. Then, this case is the union of case A and B. Then the possible combinations are:

Since there are 18+6=24 combinations, the probability is

`P(\text{Even sum or sum greater than 7)=}(24)/(36)=(4)/(6)=(2)/(3)`