Question

"A spinner with 8 equal sections labeled 1, 2, 3, 4, 5, 6, 7, 8 is used in a game. What is the theoretical probability of the given event with one spin? P(A number between 2 and 7) a) One-half b) Three-fourths c) Startfraction 5 over 8 endfraction d) Startfraction 4 over 7 endfraction"

Answer 1

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).