Final answer:
The theoretical probability of spinning a number between 2 and 7 is 5/8 assuming the spinner has numbers 1 through 8. The correct answer is option 3, which corresponds to a ⅔ chance.
Step-by-step explanation:
The question asks for the theoretical probability of spinning a number between 2 and 7 on a hypothetical spinner. Assuming the spinner has numbers 1 through 6, similar to a fair six-sided die, the numbers between 2 and 7 are 2, 3, 4, 5, and 6. There are five desired outcomes out of a total of six possible outcomes, meaning the theoretical probability is 5 out of 6 or ⅔.
No option matches ⅔, so either there is a mistake in the question or the options provided are incorrect. If the spinner had 1 through 8 instead, the numbers between 2 and 7 would be 2, 3, 4, 5, and 6, which are five desired outcomes out of eight possible outcomes, resulting in a theoretical probability of 5/8, which matches option 3.