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The spinner below shows 10 equally sized slices. Kala spun the dial 1000 times and got the following results.Outcome White Grey BlackNumber of Spins 393 291 316Fill 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:The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.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.

Question

The spinner below shows 10 equally sized slices. Kala spun the dial 1000 times and got the following results.Outcome White Grey BlackNumber of Spins 393 291 316Fill 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:The larger the number of spins, the greater the likelihood that the experimental probability will be close to the theoretical probability.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.

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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, the theoretical probability of landing on white is 1/10 = 0.100.

(b) The experimental probability of landing on white is calculated by dividing the number of times the event occurred (landing on white) by the total number of trials. Kala spun the dial 1000 times and landed on white 393 times. So, the experimental probability of landing on white is 393/1000 = 0.393.

(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 known as the Law of Large Numbers, which states that as the number of trials increases, the experimental probability tends to get closer to the theoretical probability.

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