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.
Theoretical Probability Experimental Probability Which is Greater?
2 1/6 30/120 = 1/4 Experimental Probability
3 1/6 19/120 = 0.1583 Theoretical Probability
4 1/6 25/120 = 0.2083 Theoretical Probability
5 1/6 29/120 = 0.2417 Theoretical Probability
6 1/6 17/120 = 0.1417 Theoretical Probability
To find the theoretical probability, divide the number of times the spinner landed on a particular number by the total number of spins (120).
To find the experimental probability, divide the number of times the spinner actually landed on a particular number by the total number of spins (120).
In this case, the theoretical probability of winning by landing on 2 is 1/6, while the experimental probability is 30/120 = 1/4. The experimental probability is greater than the theoretical probability.
Overall, the experimental probabilities matched closely with the theoretical probabilities in this case.