Question

read the story. the drama club at sonata middle school puts on a play every year. in the past, 75% of the shows have completely sold out. zachary is the head of the drama club this year, and he set a goal to sell out all 3 shows. how likely is it that all 3 shows will completely sell out? which simulation could be used to fairly represent the situation? roll a six - sided die 3 times. each time an even number appears, it represents a sold - out show. use a computer to randomly generate 4 numbers from 1 to 4. each time 1, 2, or 3 appears, it represents a sold - out show. create a spinner with 4 equal sections. color 1 section orange and the remaining sections purple. spin the spinner 3 times. each time the spinner lands on a purple section, it represents a sold - out show.

Explanation:

Step1: Analyze probability of sold - out shows

The probability of a show selling out in the past is 75% or $\frac{3}{4}$.

Step2: Analyze each simulation option

For rolling a six - sided die, the probability of an even number is $\frac{3}{6}=\frac{1}{2}$, not $\frac{3}{4}$.
For the spinner with 4 sections where 1 is orange and 3 are purple, the probability of landing on purple is $\frac{3}{4}$, but we need to consider the random number generation aspect for a more realistic simulation in a general sense.
For generating 4 numbers from 1 to 4 and considering 1, 2, 3 as sold - out shows, the probability of getting 1, 2, or 3 is $\frac{3}{4}$, which matches the historical probability of a show selling out, and random number generation is a common and flexible simulation method.

Answer:

Use a computer to randomly generate 4 numbers from 1 to 4. Each time 1, 2, or 3 appears, it represents a sold - out show.