Two fair dice are rolled. (a) What is the probability of getting a sum of 7? (b) What is the probability that the sum of the numbers on the dice is odd?

(a) Probability of getting a sum of 7

If two fair dice are rolled then following would be the events of getting 7:

E= [(1,6),(2,5),(3,4),(4,3),(5,2),(6,1)]

$P(E)=\frac{n(E)}{n(S)}$

When two fair dice are rolled then n(S) = 6 * 6 = 36

$P(E)=\frac{6}{36}=\frac{1}{6}=0.1667$

(b) Probability of getting a sum of odd number

Following are the possible combinations for an odd number:

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

There are total 18 possibilities of getting an add number when rolling two dice.

$P(E)=\frac{18}{36}=\frac{1}{2}=0.50$