To find the theoretical probability of spinning a number between 2 and 7 on the spinner, you need to determine how many favorable outcomes there are (numbers between 2 and 7) and divide that by the total number of possible outcomes (which is 8, as there are 8 equal sections on the spinner).
Favorable outcomes: Numbers 2, 3, 4, 5, 6, and 7 (a total of 6 numbers).
Total possible outcomes: 8 numbers on the spinner.
Now, calculate the probability:
Probability = (Number of Favorable Outcomes) / (Total Possible Outcomes)
Probability = 6 / 8
To simplify this fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 2:
Probability = (6 ÷ 2) / (8 ÷ 2)
Probability = 3/4
So, the theoretical probability of spinning a number between 2 and 7 on the spinner is **Three-fourths** (option b).