Questions: The accompanying figure shows the 36 equally likely outcomes when two balanced dice are rolled. Complete parts (a) through (d) below. Click the icon to view the figure that shows the 36 equally likely outcomes when two balanced dice are rolled. The probability that the sum of the dice is even is 0.5 (Type an integer or a decimal. Round to three decimal places as needed.) c. Determine the probability that the sum of the dice is 10 or 5. The probability that the sum of the dice is 10 or 5 is (Type an integer or a decimal. Round to three decimal places as needed.)

The accompanying figure shows the 36 equally likely outcomes when two balanced dice are rolled. Complete parts (a) through (d) below.
Click the icon to view the figure that shows the 36 equally likely outcomes when two balanced dice are rolled.

The probability that the sum of the dice is even is 0.5
(Type an integer or a decimal. Round to three decimal places as needed.)
c. Determine the probability that the sum of the dice is 10 or 5.

The probability that the sum of the dice is 10 or 5 is
(Type an integer or a decimal. Round to three decimal places as needed.)

Transcript text: The accompanying figure shows the 36 equally likely outcomes when two balanced dice are rolled. Complete parts (a) through (d) below. Click the icon to view the figure that shows the 36 equally likely outcomes when two balanced dice are rolled. The probability that the sum of the dice is even is 0.5 (Type an integer or a decimal. Round to three decimal places as needed.) c. Determine the probability that the sum of the dice is 10 or 5 . The probability that the sum of the dice is 10 or 5 is $\square$ (Type an integer or a decimal. Round to three decimal places as needed.)

Solution

Solution Steps

To determine the probability that the sum of the dice is 10 or 5, we need to count the number of outcomes where the sum is 10 or 5 and then divide by the total number of possible outcomes (which is 36).

Step 1: Total Outcomes

When rolling two balanced dice, the total number of possible outcomes is given by $ 6 \times 6 = 36 $.

Step 2: Favorable Outcomes for Sum of 10

The pairs of dice that yield a sum of 10 are:

$ (4, 6) $
$ (5, 5) $
$ (6, 4) $

Thus, the number of favorable outcomes for a sum of 10 is $ 3 $.

Step 3: Favorable Outcomes for Sum of 5

The pairs of dice that yield a sum of 5 are:

$ (1, 4) $
$ (2, 3) $
$ (3, 2) $
$ (4, 1) $

Thus, the number of favorable outcomes for a sum of 5 is $ 4 $.

Step 4: Total Favorable Outcomes

The total number of favorable outcomes for either a sum of 10 or 5 is: \[ 3 + 4 = 7 \]

Step 5: Probability Calculation

The probability $ P $ that the sum of the dice is either 10 or 5 is calculated as: \[ P = \frac{\text{favorable outcomes}}{\text{total outcomes}} = \frac{7}{36} \approx 0.1944 \]