Question

a disc jockey at a school dance has equal numbers of rock and country songs that she randomly selects from. she designs a simulation to estimate the probability that the next three songs she plays are all country songs. which simulation design could she use to estimate the probability? a. random digits let 1, 2, 3, 4, 5 = rock let 6, 7, 8, 9 = country select three random digits. repeat. b. number cube let 1 = rock let 2 = country roll cube three times. repeat. c. number cube let even number = rock let odd number = country roll cube three times. repeat. d. random digits let 1, 2, 3 = rock let 4, 5, 6 = country select three random digits. repeat.

Explanation:

To estimate the probability, the simulation must have equal probability for rock and country (since there are equal numbers of each). Let's analyze each option:

• Option A: Rock has 5 digits (1 - 5), country has 4 digits (6 - 9). Probabilities are not equal.
• Option B: A number cube has 6 sides, but only using 1 and 2. The remaining 4 sides (3 - 6) are unused, so the simulation doesn't account for all possible outcomes properly, and the probability of rock and country isn't equal in terms of the cube's full range.
• Option C: A number cube has 3 even and 3 odd numbers. So even (rock) and odd (country) each have a probability of $\frac{3}{6}=\frac{1}{2}$, which matches the equal number of rock and country songs. Rolling the cube three times simulates three song selections.
• Option D: Rock has 3 digits (1 - 3), country has 3 digits (4 - 6), but random digits include 0 - 9, so 0 is unaccounted for, making the probability of selecting a rock or country digit not equal to $\frac{1}{2}$ (since there are 10 digits total, 3 for rock, 3 for country, and 4 unused, so the effective probability for rock is $\frac{3}{10}$, country $\frac{3}{10}$, which is not equal to the required $\frac{1}{2}$ as the number of rock and country songs are equal).

Answer:

C. Number cube
Let even number = rock
Let odd number = country
Roll cube three times. Repeat.