Spinner results against the theoretical model

Spinner results against the theoretical model

IP 2
7 marks

A spinner is divided into three sectors: red with angle \(72^\circ\), and blue and green each with angle \(144^\circ\). Ama spins it \(200\) times and records red \(46\) times, blue \(81\) times and green \(73\) times.

  1. Use Ama's results to estimate the probability of red.[1]
  2. Find the theoretical probability of each colour, stating the assumption you make.[2]
  3. Ama says her results show the spinner is unfair. Comment on her claim.[2]
  4. Using the theoretical model, find the expected number of reds in \(500\) spins, and find the probability that a single spin does not land on blue.[2]

Solution:

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Answer:(a) \(0.23\) (b) \(0.2\), \(0.4\), \(0.4\), assuming a fair spinner (c) Close to the model; differences are within chance variation (d) \(100\) \(0.6\)

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