Problem
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 thesprobability that the next three songs she plays are all country songs. Which simulation design could she use to estimate the probability? A. Coin Let heads $(H)=$ country Let tails $(T)=$ rock or pop Toss the coin three times. Repeat. B. Number cube Let even number $=$ country Let odd number = not country Roll the cube three times. Repeat. C. 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. D. Random digits from 2 to 7 Let $2,3=$ rock Let 4,5 , country Let $6,7-$ pop Select three random digits from 2 to 7 . Repeat.
Solution
Step 1 ：Analyze each option to see if it meets the requirement of having equal probabilities for country, rock, and pop songs.
Step 2 ：Option A: Coin - Not suitable, as it has only two possible outcomes.
Step 3 ：Option B: Number cube - Not suitable, as it does not allow equal probabilities for rock and pop songs.
Step 4 ：Option C: Random digits from 0 to 9 - Suitable, as it allows equal probabilities for country, rock, and pop songs.
Step 5 ：Option D: Random digits from 2 to 7 - Not suitable, as it does not allow equal probabilities for the songs.
Step 6 ：\(\boxed{\text{Final Answer: C. Random digits from 0 to 9}}\)
