The spinner below shows 10 equally sized slices. Kala spun the dial 50 times and got the following results.Outcome Grey White BlackNumber of Spins 29 14 7Fill in the table below. Round your answers to the nearest thousandth.(a) Assuming that the spinner is fair, compute the theoretical probability of landing on white.(b) From Kala's results, compute the experimental probability of landing on white.(c) Assuming that the spinner is fair, choose the statement below that is true:With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of spins, there must be a large difference between the experimental and theoretical probabilities.With a large number of spins, there must be no difference between the experimental and theoretical probabilities.
Question
The spinner below shows 10 equally sized slices. Kala spun the dial 50 times and got the following results.Outcome Grey White BlackNumber of Spins 29 14 7Fill in the table below. Round your answers to the nearest thousandth.(a) Assuming that the spinner is fair, compute the theoretical probability of landing on white.(b) From Kala's results, compute the experimental probability of landing on white.(c) Assuming that the spinner is fair, choose the statement below that is true:With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small.With a large number of spins, there must be a large difference between the experimental and theoretical probabilities.With a large number of spins, there must be no difference between the experimental and theoretical probabilities.
Solution
(a) The theoretical probability of landing on white is calculated by dividing the number of favorable outcomes (landing on white) by the total number of outcomes. Since the spinner has 10 equally sized slices, we assume that each color (grey, white, black) has an equal chance of being landed on. Therefore, the theoretical probability of landing on white is 1/3 or approximately 0.333.
(b) The experimental probability of landing on white is calculated by dividing the number of times the event (landing on white) occurred by the total number of trials. In this case, Kala spun the dial 50 times and landed on white 14 times. Therefore, the experimental probability of landing on white is 14/50 or 0.28.
(c) The correct statement is: "With a large number of spins, there might be a difference between the experimental and theoretical probabilities, but the difference should be small." This is because, in theory, with an infinite number of spins, the experimental probability should approach the theoretical probability. However, in practice, there is always some degree of variation due to chance, so the experimental probability may not exactly match the theoretical probability, especially with a finite number of spins.
Similar Questions
A spinner with 10 equally sized slices has 4 yellow slices, 4 red slices, and 2 blue slices. Amy spun the dial 1000 times and got the following results.Outcome Yellow Red BlueNumber of Spins 408 415 177Answer the following. Round your answers to the nearest thousandths.(a)From Amy's results, compute the experimental probability of landing on blue.(b)Assuming that the spinner is fair, compute the theoretical probability of landing on blue.(c)Assuming that the spinner is fair, choose the statement below that is true.
A spinner with 9 equally sized slices is shown below. (5 slices are red, 2 are blue, and 2 are yellow.) The dial is spun and stops on a slice at random. What are the odds in favor of landing on a red slice?
Let's say there is a wheel that is split into 9 numbered sections (labelled 1 – 9). Below is the table of how many times the spinner landed on each number after numerous spins.spinner number: 1 2 3 4 5 6 7 8 9result: 12 35 72 29 40 18 9 65 42Based on this result, what is the experimental probability of the spinner landing on a 1 or 7?0.0840.0650.0370.001
There are two spinners containing only white and blue slices.Spinner A has 2 blue slices and 6 white slices.All the slices are the same size.Spinner B has 16 blue slices and 4 white slices.All the slices are the same size.Each spinner is spun.List these events from least likely to most likely.Event 1: Spinner B lands on a white slice.Event 2: Spinner A lands on a green slice.Event 3: Spinner A lands on a blue slice.Event 4: Spinner B lands on a blue or white slice.Least likely Most likelyEvent , Event , Event , Event
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow, and purple. The spinner is spun several times, and the results are recorded below:Spinner ResultsColor FrequencyRed 20Blue 9Green 19Yellow 14Purple 14Based on these results, express the probability that the next spin will land on red or green or purple as a decimal to the nearest hundredth.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.