Question

a disc jockey at a school dance has equal numbers of country, rock, and pop 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. number cube let 1, 4 = rock let 2, 5 = country let 3, 6 = pop roll the cube three times. repeat. b. coin let heads (h) = country let tails (t) = rock or pop toss the coin three times. repeat. c. number cube let even number = country let odd number = not country roll the cube three times. repeat. d. random digits from 0 to 9 let 1, 2, 3 = rock let 4, 5, 6 = country let 7, 8, 9, 0 = pop select three random digits from 0 to 9. repeat.

Explanation:

Step1: Analyze the requirements

We need a simulation with equal - probability outcomes for three types of songs (country, rock, pop).

Step2: Evaluate Option A

A number cube has 6 sides. By splitting it into three pairs (1,4 for rock; 2,5 for country; 3,6 for pop), each song type has a $\frac{2}{6}=\frac{1}{3}$ probability of being selected on each roll, which is correct as there are equal numbers of each song type in reality.

Step3: Evaluate Option B

A coin has 2 outcomes. Tossing a coin doesn't give equal probabilities for three song - types. Rock and pop are grouped together, so it's incorrect.

Step4: Evaluate Option C

A number cube's odd/even split gives two groups, not three with equal probabilities for rock, country, and pop. So it's incorrect.

Step5: Evaluate Option D

The digits 0 - 9 are split into three groups with unequal numbers of digits (3 for rock, 3 for country, 4 for pop), so the probabilities for each song type are not equal. So it's incorrect.

Answer:

A. Number cube
Let 1, 4 = rock
Let 2, 5 = country
Let 3, 6 = pop
Roll the cube three times. Repeat.