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.
Answer
\(\boxed{\text{Final Answer: C. Random digits from 0 to 9}}\)
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 ：\(\boxed{\text{Final Answer: C. Random digits from 0 to 9}}\)
