Final answer:
The experimental probability that the band will play an encore at its next show is 1/3. This probability is based on the band having played an encore at 2 of its last 6 shows.
Step-by-step explanation:
The student has provided information that a band played an encore at 2 of its last 6 shows. To calculate the experimental probability that the band will play an encore at its next show, you take the number of times the event of interest has occurred and divide it by the total number of trials. In this case, the event of interest (playing an encore) happened 2 times out of a total of 6 shows.
We can write the experimental probability as a fraction:
P(encore) = Number of encores played / Total number of shows = 2 / 6
When simplifying the fraction, we get:
P(encore) = 1 / 3
The experimental probability that the band will play an encore at the next show is therefore 1/3.
It's important to note that experimental probability is based on past events and does not guarantee future outcomes, but it can give a rough estimate of what might happen based on historical data.
When working with relative frequency and probability problems, answers should be rounded to four decimal places if necessary. However, in this particular case, the fraction 1/3 is already in its simplest form and does not require rounding.