Question

a 12 - sided solid has equal - sized faces numbered 1 to 12.
a. find p(number greater than 7).
b. find p(number less than 3).
c. is the solid fair? explain.
a. p(number greater than 7)=square%
(type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Identify total outcomes

Total faces = 12

Step2: Favorable outcomes for a

Numbers >7: 8,9,10,11,12 → 5 outcomes

Step3: Calculate probability for a

$P(\text{number >7}) = \frac{5}{12} \approx 0.4167$
Convert to percent: $0.4167 \times 100 = 41.7\%$

Step4: Favorable outcomes for b

Numbers <3: 1,2 → 2 outcomes

Step5: Calculate probability for b

$P(\text{number <3}) = \frac{2}{12} = \frac{1}{6} \approx 0.1667$
Convert to percent: $0.1667 \times 100 = 16.7\%$

Step6: Explain fairness for c

All faces are equal-sized, so each number (1-12) has an equal probability of $\frac{1}{12}$ of being rolled. Equal likelihood of all outcomes means the solid is fair.

Answer:

a. 41.7%
b. 16.7%
c. Yes, the solid is fair.