Stacy uses a spinner with six equal sections numbered 2, 2, 3, 4, 5, and 6 to play a game. Stacy spins the pointer 120 times and records the results. The pointer lands 30 times on a section numbered 2, 19 times on 3, 25 times on 4, 29 times on 5, and 17 times on 6. A winning spin is a 2.
Complete the table to find the theoretical and experimental probabilities of winning, and compare the two.
The theoretical probability of winning, or landing on a section numbered 2, can be calculated by dividing the number of favorable outcomes (1) by the total number of possible outcomes (6).
The experimental probability of winning can be calculated by dividing the number of times the pointer landed on a section numbered 2 by the total number of spins.
| Outcome | Theoretical Probability | Experimental Probability |
|-------------|--------------------------|--------------------------|
| Winning | 1/6 | 30/120 = 1/4 |
| Not Winning | 5/6 | 90/120 = 3/4 |
Therefore, the theoretical probability of winning is 1/6 or approximately 16.67%, while the experimental probability of winning is 1/4 or 25%. The experimental probability is higher than the theoretical probability because Stacy had a slightly higher chance of landing on a section numbered 2 in her actual spins compared to what was expected theoretically.