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Predictions from Random Selections: Buttons, Spinners, and Library Probabilities

In this analytical exploration, Emilio randomly selects buttons from a bag, recording their colors over 32 trials to predict future selections. Alongside, we analyze a spinner's performance after 210 spins to forecast the expected outcomes for landing on green. Additionally, we evaluate the probability of selecting a biography from a mix of picture books, mysteries, and biographies at the library. These scenarios provide a basis for understanding statistical predictions and probabilities in various contexts.

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Predictions from Random Selections: Buttons, Spinners, and Library Probabilities

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  1. Emilio has a bag containing different-colored buttons. He randomly selects a button from the bag, records its color, and puts it back. The table below shows his results after selecting 32 buttons from the bag. Based on these results, which of the following is the most reasonable prediction of the number of orange buttons Emilio will select from the bag in his next 64 tries? • 4 • 8 • 16 • 32

  2. Below is a picture of a fair spinner. If the spinner arrow was spun 210 times, how many times would it be expected to land on green? • 7 • 10 • 21 • 70

  3. There are 3 picture books, 5 mysteries, and 4 biographies in the library book drop. What is the probability that the librarian will pull out a biography?

  4. Rob whirled a spinner 60 times. The number of times the pointer landed on each color is shown in the table. • Red • Green • Yellow • Blue

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