A spinner with 5 equally sized slices has 3 red slices, 1 yellow slice, and 1 blue slice. Rachel spun the dial 500 times and got the following results.Outcome Red Yellow BlueNumber of Spins 319 102 79Answer the following. Round your answers to the nearest thousandths.(a)From Rachel's results, compute the experimental probability of landing on yellow.(b)Assuming that the spinner is fair, compute the theoretical probability of landing on yellow.(c)Assuming that the spinner is fair, choose the statement below that is true.
Question
A spinner with 5 equally sized slices has 3 red slices, 1 yellow slice, and 1 blue slice. Rachel spun the dial 500 times and got the following results.Outcome Red Yellow BlueNumber of Spins 319 102 79Answer the following. Round your answers to the nearest thousandths.(a)From Rachel's results, compute the experimental probability of landing on yellow.(b)Assuming that the spinner is fair, compute the theoretical probability of landing on yellow.(c)Assuming that the spinner is fair, choose the statement below that is true.
Solution
(a) The experimental probability of landing on yellow is calculated by dividing the number of times the spinner landed on yellow by the total number of spins. So, 102 (number of yellow spins) divided by 500 (total spins) equals 0.204. Therefore, the experimental probability of landing on yellow is 0.204.
(b) The theoretical probability of landing on yellow is calculated by dividing the number of yellow slices by the total number of slices. So, 1 (number of yellow slices) divided by 5 (total slices) equals 0.2. Therefore, the theoretical probability of landing on yellow is 0.2.
(c) Assuming that the spinner is fair, the statement that is true would be: "The theoretical probability of landing on a color is the same for all colors." This is because a fair spinner has an equal chance of landing on any given color. However, in this case, the spinner does not have an equal number of each color, so the theoretical probability is not the same for all colors.
Similar Questions
The spinner below shows 10 equally sized slices. Keiko spun the dial 150 times and got the following results.Outcome White Grey BlackNumber of Spins 68 46 36Fill 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 Keiko's results, compute the experimental probability of landing on white.(c) Assuming that the spinner is fair, choose the statement below that is true:The smaller the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.The experimental probability will never be very close to the theoretical probability, no matter the number of spins.The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.
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A certain spinner has equally sized slices. The odds in favor of landing on a red slice are 4 : 3. What is the probability of landing on a red slice?
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 8Blue 4Green 17Yellow 15Purple 3Based on these results, express the probability that the next spin will land on red or blue or green as a decimal to the nearest hundredth.
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
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