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.
Question
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.
Solution
(a) The theoretical probability of landing on white is calculated by dividing the number of white slices by the total number of slices. Since the spinner is fair and has 10 equally sized slices, the theoretical probability is 1/10 = 0.100.
(b) The experimental probability of landing on white is calculated by dividing the number of times Keiko landed on white by the total number of spins. So, the experimental probability is 68/150 = 0.453.
(c) The statement that is true is: "The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability." This is because as the number of trials increases, the experimental probability tends to get closer to the theoretical probability due to the Law of Large Numbers.
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