Question
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?
Complete the table to find the theoretical and experimental probabilities of winning, and compare the two.
Theoretical Probability Experimental Probability Which is Greater?
Answers
GPT 3.5
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.
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.