In Exercises 5.16-5.26, express your probability answers as a decimal rounded to three places.

Dice. Two balanced dice are rolled. Refer to Fig. 5.1 on page 198 and determine the probability that the sum of the dice is

(a) 6. (b) even.

(c). 7 or 11. (d) 2. 3, or 12.

The total number of all outcomes with an even sum is:

(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).

They are 18 in number.

Now Let's take the occurrence 'E' as an even sum.

The probability that the sum is even:

$$\begin{gathered} P\left(E\right)=\frac{18}{36} \\ =0.500 \end{gathered}$$

The total number of all outcomes with a sum of 7 or 11 is:

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

They are 8 in number.

Now Let's take the occurrence 'E' as a sum of 7 or 11.

The probability that the sum is 7 or 11:

$$\begin{gathered} P\left(E\right)=\frac{8}{36} \\ =0.222 \end{gathered}$$

The total number of all outcomes with a sum of 2. 3, or 12 is:

(1,1), (1,2), (6,6), (2,1)

They are 18 in number.

Now Let's take the occurrence 'E' as the sum of 2. 3, or 12.

The probability that the sum is 2. 3, or 12 is:

$$\begin{gathered} P\left(E\right)=\frac{4}{36} \\ =0.111 \end{gathered}$$